Lucas numbers (n = 1 to 100)


The definition

L0 = 2
L1 = 1
Ln = Ln-1 + Ln-2(n >=2)

Further information is here.


  n : Ln (alen)= factors

  1 : 1 (1) = unit
  2 : 3 (1) = prime
  3 : 4 (1) = 2 * 2
  4 : 7 (1) = prime
  5 : 11 (2) = prime

  6 : 18 (2) = 2 * 3 * 3
  7 : 29 (2) = prime
  8 : 47 (2) = prime
  9 : 76 (2) = 2 * 2 * 19
 10 : 123 (3) = 3 * 41

 11 : 199 (3) = prime
 12 : 322 (3) = 2 * 7 * 23
 13 : 521 (3) = prime
 14 : 843 (3) = 3 * 281
 15 : 1364 (4) = 2 * 2 * 11 * 31

 16 : 2207 (4) = prime
 17 : 3571 (4) = prime
 18 : 5778 (4) = 2 * 3 * 3 * 3 * 107
 19 : 9349 (4) = prime
 20 : 15127 (5) = 7 * 2161

 21 : 24476 (5) = 2 * 2 * 29 * 211
 22 : 39603 (5) = 3 * 43 * 307
 23 : 64079 (5) = 139 * 461
 24 : 103682 (6) = 2 * 47 * 1103
 25 : 167761 (6) = 11 * 101 * 151

 26 : 271443 (6) = 3 * 90481
 27 : 439204 (6) = 2 * 2 * 19 * 5779
 28 : 710647 (6) = 7 * 7 * 14503
 29 : 1149851 (7) = 59 * 19489
 30 : 1860498 (7) = 2 * 3 * 3 * 41 * 2521

 31 : 3010349 (7) = prime
 32 : 4870847 (7) = 1087 * 4481
 33 : 7881196 (7) = 2 * 2 * 199 * 9901
 34 : 12752043 (8) = 3 * 67 * 63443
 35 : 20633239 (8) = 11 * 29 * 71 * 911

 36 : 33385282 (8) = 2 * 7 * 23 * 103681
 37 : 54018521 (8) = prime
 38 : 87403803 (8) = 3 * 29134601
 39 : 141422324 (9) = 2 * 2 * 79 * 521 * 859
 40 : 228826127 (9) = 47 * 1601 * 3041

 41 : 370248451 (9) = prime
 42 : 599074578 (9) = 2 * 3 * 3 * 83 * 281 * 1427
 43 : 969323029 (9) = 6709 * 144481
 44 : 1568397607 (10) = 7 * 263 * 881 * 967
 45 : 2537720636 (10) = 2 * 2 * 11 * 19 * 31 * 181 * 541

 46 : 4106118243 (10) = 3 * 4969 * 275449
 47 : 6643838879 (10) = prime
 48 : 10749957122 (11) = 2 * 769 * 2207 * 3167
 49 : 17393796001 (11) = 29 * 599786069
 50 : 28143753123 (11) = 3 * 41 * 401 * 570601

 51 : 45537549124 (11) = 2 * 2 * 919 * 3469 * 3571
 52 : 73681302247 (11) = 7 * 103 * 102193207
 53 : 119218851371 (12) = prime
 54 : 192900153618 (12) = 2 * 3 * 3 * 3 * 3 * 107 * 11128427
 55 : 312119004989 (12) = 11 * 11 * 199 * 331 * 39161

 56 : 505019158607 (12) = 47 * 10745088481
 57 : 817138163596 (12) = 2 * 2 * 229 * 9349 * 95419
 58 : 1322157322203 (13) = 3 * 347 * 1270083883
 59 : 2139295485799 (13) = 709 * 8969 * 336419
 60 : 3461452808002 (13) = 2 * 7 * 23 * 241 * 2161 * 20641

 61 : 5600748293801 (13) = prime
 62 : 9062201101803 (13) =  3 * 3020733700601
 63 : 14662949395604 (14) = 2 * 2 * 19 * 29 * 211 * 1009 * 31249
 64 : 23725150497407 (14) = 127 * 186812208641
 65 : 38388099893011 (14) = 11 * 131 * 521 * 2081 * 24571

 66 : 62113250390418 (14) = 2 * 3 * 3 * 43 * 307 * 261399601
 67 : 100501350283429 (15) = 4021 * 24994118449
 68 : 162614600673847 (15) = 7 * 23230657239121
 69 : 263115950957276 (15) = 2 * 2 * 139 * 461 * 691 * 1485571
 70 : 425730551631123 (15) = 3 * 41 * 281 * 12317523121

 71 : 688846502588399 (15) = prime
 72 : 1114577054219522 (16) = 2 * 47 * 1103 * 10749957121
 73 : 1803423556807921 (16) = 151549 * 11899937029
 74 : 2918000611027443 (16) = 3 * 11987 * 81143477963
 75 : 4721424167835364 (16) = 2 * 2 * 11 * 31 * 101 * 151 * 12301 * 18451

 76 : 7639424778862807 (16) = 7 * 1091346396980401
 77 : 12360848946698171 (17) = 29 * 199 * 229769 * 9321929
 78 : 20000273725560978 (17) = 2 * 3 * 3 * 90481 * 12280217041
 79 : 32361122672259149 (17) = prime
 80 : 52361396397820127 (17) = 2207 * 23725145626561

 81 : 84722519070079276 (17) = 2 * 2 * 19 * 3079 * 5779 * 62650261
 82 : 137083915467899403 (18) = 3 * 163 * 800483 * 350207569
 83 : 221806434537978679 (18) = 35761381 * 6202401259
 84 : 358890350005878082 (18) = 2 * 7 * 7 * 23 * 167 * 14503 * 65740583
 85 : 580696784543856761 (18) = 11 * 3571 * 1158551 * 12760031

 86 : 939587134549734843 (18) = 3 * 313195711516578281
 87 : 1520283919093591604 (19) = 2 * 2 * 59 * 349 * 19489 * 947104099
 88 : 2459871053643326447 (19) = 47 * 93058241 * 562418561
 89 : 3980154972736918051 (19) = 179 * 22235502640988369
 90 : 6440026026380244498 (19) = 2 * 3 * 3 * 3 * 41 * 107 * 2521 * 10783342081

 91 : 10420180999117162549 (20) = 29 * 521 * 689667151970161
 92 : 16860207025497407047 (20) = 7 * 253367 * 9506372193863
 93 : 27280388024614569596 (20) = 2 * 2 * 63799 * 3010349 * 35510749
 94 : 44140595050111976643 (20) = 3 * 563 * 5641 * 4632894751907
 95 : 71420983074726546239 (20) = 11 * 191 * 9349 * 41611 * 87382901

 96 : 115561578124838522882 (21) = 2 * 1087 * 4481 * 11862575248703
 97 : 186982561199565069121 (21) = 3299 * 56678557502141579
 98 : 302544139324403592003 (21) = 3 * 281 * 5881 * 61025309469041
 99 : 489526700523968661124 (21) = 2 * 2 * 19 * 199 * 991 * 2179 * 9901 * 1513909
100 : 792070839848372253127 (21) = 7 * 2161 * 9125201 * 5738108801

What's new index Numbers still not completely factored

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima