

A020137


Pseudoprimes to base 8.


8



9, 21, 45, 63, 65, 105, 117, 133, 153, 231, 273, 341, 481, 511, 561, 585, 645, 651, 861, 949, 1001, 1105, 1281, 1365, 1387, 1417, 1541, 1649, 1661, 1729, 1785, 1905, 2047, 2169, 2465, 2501, 2701, 2821, 3145, 3171, 3201, 3277, 3605, 3641, 4005, 4033, 4097
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OFFSET

1,1


COMMENTS

This sequence is a subsequence of the sequence A122785. In fact the terms are odd composite terms of A122785. Theorem: If both numbers q and 2q1 are primes (q is in the sequence A005382) and n=q*(2q1) then 8^(n1)==1 (mod n) (n is in the sequence) iff q is of the form 12k+1. 2701,18721,49141,104653,226801,665281,721801,... is the related subsequence. This subsequence is also a subsequence of the sequence A122785.  Farideh Firoozbakht, Sep 15 2006
Composite numbers k such that 8^(k1) == 1 (mod k).  Michel Lagneau, Feb 18 2012
If q and 3q2 are odd primes, then q*(3q2) is in the sequence.  Davide Rotondo, May 25 2021


LINKS



MATHEMATICA

Select[Range[4100], ! PrimeQ[ # ] && PowerMod[8, (#  1), # ] == 1 &] (* Farideh Firoozbakht, Sep 15 2006 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



