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A268210

Primes p of the form 2^k + 1 such that p - k is a prime q (for k >= 0).

2, 3, 5, 17, 65537

OFFSET

1,1

COMMENTS

Intersection of A092506 and A268209.

Sequence is not the same as A004249 because A004249(5) is a composite number.

Corresponding values of numbers k: 0, 1, 2, 4, 16; corresponding values of primes q: 2, 2, 3, 13, 65521.

4 out of 5 known Fermat primes from A019434 (3, 5, 17, 65537) are terms.

LINKS

EXAMPLE

Prime 17 = 2^4 + 1 is a term because 17 - 4 = 13 (prime).

257 = 2^8 + 1 is not a term because 257 - 8 = 249 (composite number).

MATHEMATICA

2^# + 1 &@ Select[Range[0, 600], PrimeQ[2^# + 1] && PrimeQ[2^# - # + 1] &] (* Michael De Vlieger, Jan 29 2016 *)

PROG

(Magma) [2^k + 1: k in [0..60] | IsPrime(2^k + 1) and IsPrime(2^k - k + 1)];

CROSSREFS

KEYWORD

nonn

AUTHOR

STATUS

approved

URL: https://oeis.org/A268210