A345214 Primes p such that the sum of 2^k for k such that 2^k < p and p+2^k is prime is greater than p.

67, 73, 149, 641, 659, 1039, 1063, 1087, 1117, 2081, 2111, 2153, 2459, 2549, 4201, 4273, 4327, 4447, 4567, 4903, 5077, 5107, 8219, 8501, 8537, 8819, 8861, 8999, 9011, 9209, 9239, 10061, 10331, 16417, 16447, 16573, 16603, 16927, 16963, 16993, 17389, 17467, 17977, 18757, 19777, 20143, 20563, 21487

Offset

1,1

Links

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

Example

a(4) = 641 is a member because 641+2 = 643, 641+32 = 673, 641+128 = 769 and 641+512=1153 are prime and 2+32+128+512 = 674 > 641.

Maple

filter:= proc(p) local i;
  convert(select(t -> isprime(p+t), [seq(2^i, i=1..ilog2(p))]), `+`) > p
end proc:
select(filter, [seq(ithprime(i), i=1..10000)]);

Mathematica

filterQ[p_] := Total@Select[2^Range[Length[IntegerDigits[p, 2]]-1], PrimeQ[p+#]&] > p;
Select[Prime[Range[10000]], filterQ] (* _Jean-François Alcover_, Jun 11 2021 *)

Crossrefs

Sequence in context: A033243 A241897 A225626 * A277429 A039432 A043255

Adjacent sequences: A345211 A345212 A345213 * A345215 A345216 A345217

Keyword

nonn

Author

_J. M. Bergot_ and _Robert Israel_, Jun 10 2021

Status

approved