A020136 Fermat pseudoprimes to base 4.

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

Offset

1,1

Comments

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) form a subsequence (cf. A129521). - Farideh Firoozbakht, Sep 12 2006

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

Composite numbers n such that 4^(n-1) == 1 (mod n). - Michel Lagneau, Feb 18 2012

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

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)^(n-1)==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