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A020137 Pseudoprimes to base 8. 7
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 (list; graph; refs; listen; history; text; internal format)
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 & 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 n such that 8^(n-1) == 1 (mod n). [From Michel Lagneau, Feb 18 2012]

LINKS

R. J. Mathar  and T. D. Noe, Table of n, a(n) for n = 1..1000 (R. J. Mathar to 613 terms)

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: A110680 A163205 A154862 * A231570 A020190 A225507

Adjacent sequences:  A020134 A020135 A020136 * A020138 A020139 A020140

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified September 26 01:25 EDT 2017. Contains 292500 sequences.