A244913 Primes prime(k) such that 2^(k-1) - prime(k) is also prime.

11, 13, 17, 19, 23, 37, 61, 233, 257, 1553, 2879, 4919, 6389, 7621, 8081, 35593, 37951, 96263, 206419, 596803, 1202837, 2837851

Offset: 1

Author

Robert G. Wilson v, Jul 09 2014

Keywords

• nonn
• more

Comments

a(22) > 1211303. - J.W.L. (Jan) Eerland, Dec 08 2022

a(23) > 3000000. - Michael S. Branicky, Jun 03 2025

Crossrefs

Cf. A078686, A227126.

Programs

Maple

for i from 1 do
    p := ithprime(i) ;
    if isprime(2^(numtheory[pi](p-1))-p) then
        printf("%d,\n",p) ;
    end if;
end do: # R. J. Mathar, Jul 11 2014

Mathematica

p = 2; lst = {}; While[p < 800001, If[ PrimeQ[ 2^(PrimePi@ p-1) - p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst
n=1;Monitor[Parallelize[While[True,If[PrimeQ[2^(PrimePi[Prime[n]-1])-Prime[n]],Print[Prime[n]]];n++];n],n] (* J.W.L. (Jan) Eerland, Dec 08 2022 *)

PARI

is(n)=isprime(n) && isprime(2^primepi(n-1)-n) \\ Charles R Greathouse IV, Feb 25 2017

Formula

{p in A000040: 2^[A000720(p-1)]-p in A000040}. - R. J. Mathar, Jul 11 2014

Extensions

a(21) from J.W.L. (Jan) Eerland, Dec 08 2022

a(22) from Michael S. Branicky, Jun 02 2025