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
Keywords
Examples
10^27-1 = 3^5*37*757*333667*440334654777631 is a solution to the congruence.
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).
Programs
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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 *) -
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
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
Extensions
Edited by Max Alekseyev, Nov 16 2005
Edited by Hans Havermann, Jul 11 2014