A242944 - OEIS

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

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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