A378703 Primes p such that 2^(nextprime(p) - p) + p is prime.

3, 7, 13, 37, 43, 67, 73, 97, 139, 163, 223, 277, 283, 337, 367, 409, 463, 487, 547, 577, 643, 709, 733, 757, 787, 823, 937, 967, 1033, 1039, 1069, 1087, 1093, 1117, 1123, 1201, 1213, 1237, 1249, 1303, 1327, 1399, 1423, 1483, 1543, 1567, 1597, 1657, 1693, 1747, 1873, 1879

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

3 is in the sequence because 2^(nextprime(3) - 3) + 3 = 2^(5 - 3) + 3 = 2^2 + 3 = 4 + 3 = 7 is prime number.

Mathematica

Select[Prime[Range[300]], PrimeQ[2^(NextPrime[#]-#)+#] &] (* Stefano Spezia, Dec 06 2024 *)

Prog

(Magma) [p: p in PrimesUpTo(2000) | IsPrime(2^(NextPrime(p)-p)+p)];
(PARI) is(k) = isprime(k) && isprime(1 << (nextprime(k+1) - k) + k); \\ Amiram Eldar, Dec 06 2024

Crossrefs

Cf. A000040, A218075.

Sequence in context: A023212 A106952 A106951 * A106057 A049492 A166283

Adjacent sequences: A378700 A378701 A378702 * A378704 A378705 A378706

Keyword

nonn,new

Author

Juri-Stepan Gerasimov, Dec 04 2024

Status

approved