A358087 Primes that can be written as 2^x - p where p is a prime and x is a multiple of p.

2, 5, 61, 509, 1019, 4093, 8179, 524269, 1048571, 16777213, 2596148429267413814265248164610011, 1361129467683753853853498429727072845819, 1427247692705959881058285969449495136382746619, 1427247692705959881058285969449495136382746621, 45671926166590716193865151022383844364247891937

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 30 2022

Keywords

• nonn

Examples

			a(3) = 61 is a term because 61 = 2^6 - 3 where 61 and 3 are prime and 6 is divisible by 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..29

Crossrefs

Contains A057678.

Cf. A358079.

Programs

Maple

R:= NULL: count:= 0:
for k from 1 while count < 20 do
  P:= sort(convert(numtheory:-factorset(k),list),`>`);
  for p in P do
    x:= 2^k-p;
    if isprime(x) then R:= R,x; count:= count+1; fi
od od:
R;