A268209 -id:A268209 - cp's OEIS frontend

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

Jaroslav Krizek, Jan 28 2016

nonn

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.

			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).

Cf. A004249, A019434, A092506, A100361, A100362, A268209.

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

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

A268211 Numbers n of the form 2^k + 1 such that n + k is a prime q (for k >= 0).

Original entry on oeis.org

2, 5, 65, 110427941548649020598956093796432407239217743554726184882600387580788737

Offset: 1

Jaroslav Krizek, Jan 28 2016

nonn

Subsequence of A000051.
Corresponding values of numbers k are in A100359 (numbers n such that 2^n+n+1 is prime).
Corresponding values of primes q are in A061421 (primes of the form 2^n+n+1).

			65 = 2^6 + 1 is a term because 65 + 6 = 71 (prime).

Cf. A061421, A100359, A268209.

[2^n + 1: n in [0..600] | IsPrime(2^n + n + 1)]

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

a(n) = A061421(n) - A100359(n).

cp's OEIS Frontend

A268210 Primes p of the form 2^k + 1 such that p - k is a prime q (for k >= 0).

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