

A020136


Fermat pseudoprimes to base 4.


13



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

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) form a subsequence (cf. A129521).  Farideh Firoozbakht, Sep 12 2006
Primes q and 2q1 are a Cunningham chain of the second kind.  Walter Nissen, Sep 07 2009
Composite numbers n such that 4^(n1) == 1 (mod n).  Michel Lagneau, Feb 18 2012


LINKS

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


MATHEMATICA

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


PROG

(PARI) isok(n) = (Mod(4, n)^(n1)==1) && !isprime(n) && (n>1); \\ Michel Marcus, Apr 27 2018


CROSSREFS

Subsequence of A122781.
Contains A001567 (Fermat pseudoprimes to base 2) as a subsequence.
Cf. A005382, A129521.
Sequence in context: A279740 A281189 A206383 * A176033 A067401 A206169
Adjacent sequences: A020133 A020134 A020135 * A020137 A020138 A020139


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



