A063799 Numbers k such that (k+3, k+5, k+17, k+257, k+65537) are all primes.

14, 26, 176, 806, 1604, 1994, 2264, 3254, 3326, 4226, 4646, 9716, 9854, 11486, 13994, 15644, 15884, 17186, 19424, 21584, 22274, 23054, 25166, 25304, 26696, 30386, 34124, 34256, 36524, 37304, 42176, 43784, 49664, 53144, 56906, 58436

Offset

1,1

Comments

3, 5, 17 and 65537 are the known Fermat primes (see A019434).

The counting function p(N) seems to follows the law: p(N)~c*N^(gamma) where c is a positive constant and gamma the Euler function. If so the sequence should be infinite.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

a(1)=14 because 14+3 = 17, 14+5 = 19, 14+17 = 31, 14+257 = 271, 14+65537 = 65551 are all primes.

Prog

(PARI) { n=0; for (m=1, 10^9, if(isprime(m + 3) && isprime(m + 5) && isprime(m + 17) && isprime(m + 257) && isprime(m + 65537), write("b063799.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 31 2009

Crossrefs

Cf. A019434.

Sequence in context: A155505 A086258 A372008 * A086451 A190991 A306985

Adjacent sequences: A063796 A063797 A063798 * A063800 A063801 A063802

Keyword

easy,nonn

Author

Felice Russo, Aug 20 2001

Status

approved