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A345239
Primes p such that p+2^k is composite for all k with 2^k < p.
2
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jun 11 2021
STATUS
approved