

A020136


Pseudoprimes to base 4.


5



15, 85, 91, 341, 435, 451, 561, 645, 703, 1105, 1247, 1271, 1387, 1581, 1695, 1729, 1891, 1905, 2047, 2071, 2465, 2701, 2821, 3133, 3277, 3367, 3683, 4033, 4369, 4371, 4681, 4795, 4859, 5461, 5551, 6601, 6643, 7957, 8321, 8481, 8695, 8911, 9061, 9131
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OFFSET

1,1


COMMENTS

Primes q and 2q1 are a Cunningham chain of the second kind. [From Walter Nissen, Sep 07 2009]
Composite numbers n such that 4^(n1) == 1 (mod n). [From Michel Lagneau, Feb 18 2012]


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for sequences related to pseudoprimes
Eric Weisstein's World of Mathematics, Fermat Pseudoprime
Chris Caldwell, Cunningham chain [From Walter Nissen, Sep 07 2009]
Chris Caldwell, et al., Top Twenty Cunningham Chains (2nd kind) [From Walter Nissen, Sep 07 2009]


FORMULA

Theorem: If q and 2q1 are odd primes then n=q*(2q1) is in the sequence. So for n>1 A005382(n)*(2*A005382(n)1) is in the sequence  15, 91, 703, 1891, 2701, 12403, 18721, ... is the related subsequence.  Farideh Firoozbakht, Sep 12 2006


MATHEMATICA

Select[Range[9200], ! PrimeQ[ # ] && PowerMod[4, #  1, # ] == 1 &] (* Farideh Firoozbakht, Sep 12 2006 *)


CROSSREFS

Cf. A001567 (pseudoprimes to base 2), A005382, A122781.
Sequence in context: A050405 A241220 A206383 * A176033 A067401 A206169
Adjacent sequences: A020133 A020134 A020135 * A020137 A020138 A020139


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



