A242944 Primes p_i such that p_i + 2^i 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

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

Robert G. Wilson v, Table of n, a(n) for n = 1..26

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

Cf. A078686, A056206, A243428.

Sequence in context: A061245 A361898 A230139 * A137355 A147143 A006034

Adjacent sequences: A242941 A242942 A242943 * A242945 A242946 A242947

Keyword

nonn,more

Author

Robert G. Wilson v, Jun 20 2014

Status

approved