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

Author

David W. Wilson

Keywords

• nonn

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

Crossrefs

Subsequence of A122781.

Contains A001567 (Fermat pseudoprimes to base 2) as a subsequence.

Cf. A005382, A129521.

Programs

Mathematica

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

PARI

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