1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
|
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="70.538ex" height="6.176ex" style="vertical-align: -2.505ex;" viewBox="0 -1580.7 30370.2 2659.1" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title">
<title id="MathJax-SVG-1-Title">f left-parenthesis n right-parenthesis equals left floor n plus 1 plus log Subscript phi Baseline left-parenthesis StartRoot 5 EndRoot left-parenthesis n plus 1 plus log Subscript phi Baseline left-parenthesis StartRoot 5 EndRoot left-parenthesis n plus 1 right-parenthesis right-parenthesis right-parenthesis minus 5 plus StartFraction 3 Over n plus 1 EndFraction right-parenthesis minus 2 right floor</title>
<defs aria-hidden="true">
<path stroke-width="1" id="E1-MJMATHI-66" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z"></path>
<path stroke-width="1" id="E1-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path>
<path stroke-width="1" id="E1-MJMATHI-6E" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path>
<path stroke-width="1" id="E1-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path>
<path stroke-width="1" id="E1-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path>
<path stroke-width="1" id="E1-MJMAIN-230A" d="M174 734Q174 735 175 737T177 740T180 744T184 747T189 749T196 750Q206 748 214 735V-210H310H373Q401 -210 411 -213T422 -230T411 -247T369 -251Q362 -251 338 -251T298 -250H190Q178 -246 174 -234V734Z"></path>
<path stroke-width="1" id="E1-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path>
<path stroke-width="1" id="E1-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path>
<path stroke-width="1" id="E1-MJMAIN-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z"></path>
<path stroke-width="1" id="E1-MJMAIN-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path>
<path stroke-width="1" id="E1-MJMAIN-67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z"></path>
<path stroke-width="1" id="E1-MJMATHI-3C6" d="M92 210Q92 176 106 149T142 108T185 85T220 72L235 70L237 71L250 112Q268 170 283 211T322 299T370 375T429 423T502 442Q547 442 582 410T618 302Q618 224 575 152T457 35T299 -10Q273 -10 273 -12L266 -48Q260 -83 252 -125T241 -179Q236 -203 215 -212Q204 -218 190 -218Q159 -215 159 -185Q159 -175 214 -2L209 0Q204 2 195 5T173 14T147 28T120 46T94 71T71 103T56 142T50 190Q50 238 76 311T149 431H162Q183 431 183 423Q183 417 175 409Q134 361 114 300T92 210ZM574 278Q574 320 550 344T486 369Q437 369 394 329T323 218Q309 184 295 109L286 64Q304 62 306 62Q423 62 498 131T574 278Z"></path>
<path stroke-width="1" id="E1-MJSZ3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path>
<path stroke-width="1" id="E1-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path>
<path stroke-width="1" id="E1-MJMAIN-221A" d="M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z"></path>
<path stroke-width="1" id="E1-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path>
<path stroke-width="1" id="E1-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path>
<path stroke-width="1" id="E1-MJSZ3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path>
<path stroke-width="1" id="E1-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path>
<path stroke-width="1" id="E1-MJMAIN-230B" d="M229 734Q229 735 230 737T232 740T235 744T239 747T244 749T251 750Q262 748 269 735V-235Q266 -240 256 -249L147 -250H77Q43 -250 32 -247T21 -230T32 -213T72 -209Q79 -209 99 -209T133 -210H229V734Z"></path>
<path stroke-width="1" id="E1-MJSZ3-230A" d="M246 -949V1450H308V-887H571V-949H246Z"></path>
<path stroke-width="1" id="E1-MJSZ3-230B" d="M274 -887V1450H336V-949H11V-887H274Z"></path>
</defs>
<g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true">
<use xlink:href="#E1-MJMATHI-66" x="0" y="0"></use>
<use xlink:href="#E1-MJMAIN-28" x="550" y="0"></use>
<use xlink:href="#E1-MJMATHI-6E" x="940" y="0"></use>
<use xlink:href="#E1-MJMAIN-29" x="1540" y="0"></use>
<use xlink:href="#E1-MJMAIN-3D" x="2207" y="0"></use>
<g transform="translate(3264,0)">
<use xlink:href="#E1-MJSZ3-230A"></use>
<g transform="translate(583,0)">
<use xlink:href="#E1-MJMATHI-6E" x="0" y="0"></use>
<use xlink:href="#E1-MJMAIN-2B" x="822" y="0"></use>
<use xlink:href="#E1-MJMAIN-31" x="1823" y="0"></use>
<use xlink:href="#E1-MJMAIN-2B" x="2546" y="0"></use>
<g transform="translate(3546,0)">
<use xlink:href="#E1-MJMAIN-6C"></use>
<use xlink:href="#E1-MJMAIN-6F" x="278" y="0"></use>
<use xlink:href="#E1-MJMAIN-67" x="779" y="0"></use>
<use transform="scale(0.707)" xlink:href="#E1-MJMATHI-3C6" x="1809" y="-343"></use>
</g>
<use xlink:href="#E1-MJSZ3-28" x="5389" y="-1"></use>
<g transform="translate(6125,0)">
<use xlink:href="#E1-MJMAIN-221A" x="0" y="-2"></use>
<rect stroke="none" width="500" height="60" x="833" y="739"></rect>
<use xlink:href="#E1-MJMAIN-35" x="833" y="0"></use>
</g>
<use xlink:href="#E1-MJMAIN-28" x="7459" y="0"></use>
<use xlink:href="#E1-MJMATHI-6E" x="7849" y="0"></use>
<use xlink:href="#E1-MJMAIN-2B" x="8671" y="0"></use>
<use xlink:href="#E1-MJMAIN-31" x="9672" y="0"></use>
<use xlink:href="#E1-MJMAIN-2B" x="10395" y="0"></use>
<g transform="translate(11396,0)">
<use xlink:href="#E1-MJMAIN-6C"></use>
<use xlink:href="#E1-MJMAIN-6F" x="278" y="0"></use>
<use xlink:href="#E1-MJMAIN-67" x="779" y="0"></use>
<use transform="scale(0.707)" xlink:href="#E1-MJMATHI-3C6" x="1809" y="-343"></use>
</g>
<use xlink:href="#E1-MJMAIN-28" x="13238" y="0"></use>
<g transform="translate(13627,0)">
<use xlink:href="#E1-MJMAIN-221A" x="0" y="-2"></use>
<rect stroke="none" width="500" height="60" x="833" y="739"></rect>
<use xlink:href="#E1-MJMAIN-35" x="833" y="0"></use>
</g>
<use xlink:href="#E1-MJMAIN-28" x="14961" y="0"></use>
<use xlink:href="#E1-MJMATHI-6E" x="15351" y="0"></use>
<use xlink:href="#E1-MJMAIN-2B" x="16174" y="0"></use>
<use xlink:href="#E1-MJMAIN-31" x="17174" y="0"></use>
<use xlink:href="#E1-MJMAIN-29" x="17675" y="0"></use>
<use xlink:href="#E1-MJMAIN-29" x="18064" y="0"></use>
<use xlink:href="#E1-MJMAIN-29" x="18454" y="0"></use>
<use xlink:href="#E1-MJMAIN-2212" x="19066" y="0"></use>
<use xlink:href="#E1-MJMAIN-35" x="20066" y="0"></use>
<use xlink:href="#E1-MJMAIN-2B" x="20789" y="0"></use>
<g transform="translate(21790,0)">
<g transform="translate(120,0)">
<rect stroke="none" width="1449" height="60" x="0" y="220"></rect>
<use transform="scale(0.707)" xlink:href="#E1-MJMAIN-33" x="774" y="651"></use>
<g transform="translate(60,-417)">
<use transform="scale(0.707)" xlink:href="#E1-MJMATHI-6E" x="0" y="0"></use>
<use transform="scale(0.707)" xlink:href="#E1-MJMAIN-2B" x="600" y="0"></use>
<use transform="scale(0.707)" xlink:href="#E1-MJMAIN-31" x="1379" y="0"></use>
</g>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x="23479" y="-1"></use>
<use xlink:href="#E1-MJMAIN-2212" x="24437" y="0"></use>
<use xlink:href="#E1-MJMAIN-32" x="25438" y="0"></use>
</g>
<use xlink:href="#E1-MJSZ3-230B" x="26522" y="-1"></use>
</g>
</g>
</svg>
|
