A345239 Primes p such that p+2^k is composite for all k with 2^k < p.

61, 83, 113, 139, 257, 271, 353, 383, 409, 647, 751, 773, 787, 829, 953, 991, 1069, 1307, 1321, 1409, 1433, 1553, 1583, 1627, 1699, 1789, 1801, 1811, 1907, 1913, 1973, 2029, 2069, 2131, 2297, 2311, 2371, 2417, 2447, 2477, 2551, 2633, 2693, 2719, 2731, 2777, 2791, 2837, 2851, 2897, 2917, 2927

Offset

1,1

Comments

Prime(k) for k such that A345238(k)=0.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 113 is a term because 113+2, 113+2^2, ..., 113+2^6 are all composite and 2^7 > 113.

Maple

f:= proc(p) local k;
  nops(select(isprime, [seq(p+2^k, k=1..ilog2(p))]))
end proc:
select(f=0, [seq(ithprime(i), i=2..1000)]);

Mathematica

q[n_] := Module[{r = 2}, While[r < n && CompositeQ[n + r], r *= 2]; r > n]; Select[Range[3000], PrimeQ[#] && q[#] &] (* Amiram Eldar, Jun 11 2021 *)

Crossrefs

Cf. A345238.

Sequence in context: A325076 A353598 A253232 * A245759 A186457 A103812

Adjacent sequences: A345236 A345237 A345238 * A345240 A345241 A345242

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jun 11 2021

Status

approved