A066364 Prime divisors of solutions to 10^n == 1 (mod n).

3, 37, 163, 757, 1999, 5477, 8803, 9397, 13627, 15649, 36187, 40879, 62597, 106277, 147853, 161839, 215893, 231643, 281683, 295759, 313471, 333667, 338293, 478243, 490573, 607837, 647357, 743933, 988643, 1014877, 1056241, 1168711, 1353173, 1390757, 1487867, 1519591, 1627523, 1835083, 1912969, 2028119, 2029759, 2064529

Offset

1,1

Links

Max Alekseyev and Hans Havermann (Max Alekseyev to 501), Table of n, a(n) for n = 1..2060

Rüdiger Jehn and Kester Habermann, Properties of terms of OEIS A342810, arXiv:2106.05866 [math.GM], 2021.

Makoto Kamada, Factorizations of 11...11 (Repunit).

Formula

A prime p is a term iff all prime divisors of ord_p(10) are terms, where ord_p(10) is the order of 10 modulo p. - Max Alekseyev, Nov 16 2005

Example

10^27-1 = 3^5*37*757*333667*440334654777631 is a solution to the congruence.

Mathematica

fQ[p_] := Block[{fi = First@# & /@ FactorInteger[ MultiplicativeOrder[ 10, p]]}, Union[ MemberQ[ lst, #] & /@ fi] == {True}]; k = 4; lst = {3}; While[k < 180000, If[ p = Prime@ k; fQ@ p, AppendTo[ lst, p]; Print@ p]; k++]; lst (* Robert G. Wilson v, Nov 30 2013 *)

Prog

(PARI) S=Set([3]); forprime(p=7, 10^6, v=factorint(znorder(Mod(10, p)))[, 1]; if(length(setintersect(S, Set(v)))==length(v), S=setunion(S, [p])) ); print(vecsort(eval(S))) } \\ Max Alekseyev, Nov 16 2005

Crossrefs

Cf. A014950, A001270, A027889, A007138, A114207.

Sequence in context: A046867 A154823 A109835 * A106995 A120076 A119938

Adjacent sequences: A066361 A066362 A066363 * A066365 A066366 A066367

Keyword

nonn

Author

Vladeta Jovovic, Dec 21 2001

Extensions

Edited by Max Alekseyev, Nov 16 2005

Edited by Hans Havermann, Jul 11 2014

Status

approved