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

1,1

Comments

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, ..., .

Links

Table of n, a(n) for n=1..28.

Mathematica

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 *)

Crossrefs

Corresponding k are in A077375.

Cf. A078583, A078686, A056206, A243428.

Sequence in context: A361898 A387629 A230139 * A137355 A147143 A006034

Adjacent sequences: A242941 A242942 A242943 * A242945 A242946 A242947

Keyword

nonn,more

Author

Robert G. Wilson v, Jun 20 2014

Extensions

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

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

Status

approved