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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes q and 2q-1 are a Cunningham chain of the second kind. [From Walter Nissen, Sep 07 2009]

Composite numbers n such that 4^(n-1) == 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 2q-1 are odd primes then n=q*(2q-1) 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

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Last modified April 24 01:35 EDT 2014. Contains 240947 sequences.