A243428 -id:A243428 - cp's OEIS frontend

A242944 Primes prime(k) such that 2^k + prime(k) is also prime.

3, 5, 7, 11, 37, 41, 43, 83, 269, 577, 1429, 1433, 2063, 2549, 8353, 10639, 15299, 16927, 18637, 20201, 24007, 30097, 34039, 41777, 146609, 394249, 839203, 2955319

Offset: 1

Robert G. Wilson v, Jun 20 2014

If instead we ask for odd primes, and therefore the index is one less than that for all primes, the sequence would begin: 3, 29, 89, 251, 659, 937, 1307, 1453, 8179, 9391, 12097, 28499, 83969, 101209, 120739, ..., .

If we count 1 amongst the primes (A008578), then the sequence would begin: 1, 3, 31, 71, 97, 107, 277, 307, 641, 907, 967, 1009, 1447, 3463, 3527, 7757, 8167, ..., .

Corresponding k are in A077375.

Cf. A078583, A078686, A056206, A243428.

p = 2; lst = {}; While[p < 760001, If[ PrimeQ[p + 2^PrimePi@ p], AppendTo[ lst, p]; Print@ p]; p = NextPrime@ p; c++]; lst
Select[Table[{n,Prime[n]},{n,3000}],PrimeQ[#[[2]]+2^#[[1]]]&][[;;,2]] (* The program generates the first 21 terms of the sequence. *) (* Harvey P. Dale, Mar 04 2024 *)

a(27) from Michael S. Branicky, May 29 2025 using A077375.

a(28) from Michael S. Branicky, Jun 01 2025

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A242944 Primes prime(k) such that 2^k + prime(k) is also prime.

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