1,1

Comments from Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 31 2007: (Start)

a(n) > n.

Numbers n>1 such that a(n-1) = n are listed in A015951 = {1, 2, 3, 9, 21, 26, 27, 63, 81, ...} Numbers n such that n | 5^n + 1.

a(59)-a(77) = {30359, 1495, 188, 63, 841, 14509, 70, 276391, 98, 1083, 556, 169, 34161, 251569, 92, 18003, 175, 23501, 442}.

a(79)-a(143) = {5782, 81, 88, 8371, 273, 1536803, 95, 87659, 649481, 5767, 268, 3035, 5178, 4089, 506, 2972023, 505, 1099, 264, 1147, 1963, 275, 524, 333017, 858, 231, 260, 335441, 531, 9779, 172, 335, 64786, 247, 187, 253, 203, 1953009, 508, 1271, 19657063, 3005, 424, 221, 266, 847, 129, 671, 246, 265467, 496, 2995, 4333, 3588307, 164, 171, 610, 1169, 152, 149747, 174, 285, 300028, 2771, 287}.

a(145)-a(153) = {170, 147, 1243, 78001, 713, 21833, 3206, 553, 236}.

a(155)-a(171) = {165, 13500637, 204, 289, 451, 2965, 481, 96119, 594, 1547, 185, 259, 357, 1067, 232, 985, 6362077}.

a(173)-a(182) = {452, 282113, 295, 269639, 184, 667, 26307, 1457, 234, 617367}.

a(185)-a(203) = {344, 13324807, 498, 189, 436, 2795, 1333, 3421, 224, 1007, 1030, 209, 428, 1819, 329, 325, 212, 940643, 1826}.

a(n)>25*10^6 for n = {16,22,58,78,119,144,154,172,183,184,...}. (End)

Do[k = 1; While[PowerMod[5, k, k] != n, k++ ]; Print[k], {n, 30}]

t = Table[0, {1000} ]; k = 1; While[ k < 200000000, a = PowerMod[5, k, k]; If[a < 1001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t

Cf. A015951, A036236, A078457, A119678, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821.

Sequence in context: A114996 A137077 A046965 this_sequence A130846 A114101 A114007

Adjacent sequences: A119676 A119677 A119678 this_sequence A119680 A119681 A119682

nonn

Ryan Propper (rpropper(AT)stanford.edu), Jun 12 2006

a(58) <= 16860204577843069 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 06 2007

Revised by Max Alekseyev (maxal(AT)cs.ucsd.edu), Sep 25 2007