

A066364


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


8



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
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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

10^271 = 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



