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A020137
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Pseudoprimes to base 8.
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8
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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
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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Select[Range[4100], ! PrimeQ[ # ] && PowerMod[8, (# - 1), # ] == 1 &] (* Farideh Firoozbakht, Sep 15 2006 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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