

A020136


Pseudoprimes to base 4.


10



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



