A020137 - OEIS

A020137

Pseudoprimes to base 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 2q-1 are primes (q is in the sequence A005382) and n=q*(2q-1) then 8^(n-1)==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^(k-1) == 1 (mod k). - Michel Lagneau, Feb 18 2012

If q and 3q-2 are odd primes, then q*(3q-2) is in the sequence. - Davide Rotondo, May 25 2021

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..613 from R. J. Mathar, terms 614..1000 from T. D. Noe)

Index entries for sequences related to pseudoprimes

MATHEMATICA

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

CROSSREFS

Cf. A001567 (pseudoprimes to base 2), A005382, A122783, A122785.

Sequence in context: A163205 A154862 A350632 * A231570 A020190 A225507

Adjacent sequences: A020134 A020135 A020136 * A020138 A020139 A020140

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved