A244913 -id:A244913 - cp's OEIS frontend

A227126 Primes prime(k) such that 2^(k+1) - prime(k) is also prime.

2, 3, 5, 11, 17, 167, 193, 197, 433, 4111, 9173, 42929, 95279, 98897, 139409, 142567, 228617, 329333, 344209, 791191, 829177, 1274509, 1284037, 2432791, 2443741

Offset: 1

Gerasimov Sergey, Jul 02 2013

The corresponding primes 2^(k + 1) - prime(k) are 2, 5, 11, 53, 239, 1099511627609, 35184372088639, ...

The prime indices k are 1, 2, 3, 5, 7, 39, 44, 45, 84, 566, 1137, ...

			5 is a term because 5 is the 3rd prime, and 2^(3+1) - 5 = 16 - 5 = 11 which is a prime
11 is in the sequence because 11 = prime(5) and 2^(5 + 1) - 11 = 64 - 11 = 53 is a prime.

Cf. A078686, A244913, A244916, A242944, A228021.

p = 2; lst = {}; While[p < 850001, If[ PrimeQ[ 2^(PrimePi@ p +1) - p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst (* Robert G. Wilson v, Jul 09 2014 *)

lista(nn) = {ip = 1; forprime(p=2, nn, if (isprime(2^(ip+1)-p), print1(p, ", ")); ip++;);} \\ Michel Marcus, Jul 12 2014

a(3), a(6), a(8)-a(12) from Joerg Arndt, Jul 03 2013
Corrected and extended through a(21) by Robert G. Wilson v, Jul 09 2014
Entry revised by N. J. A. Sloane, Jan 02 2019, incorporating data from a later submission from Robert G. Wilson v
a(22)-a(25) from Michael S. Branicky, May 31 2025

A228021 Prime(k) such that 2^(k - 1) + prime(k) is also prime.

Original entry on oeis.org

2, 3, 29, 89, 251, 659, 937, 1307, 1453, 8179, 9391, 12097, 28499, 83969, 101209, 120739, 730993

Offset: 1

Juri-Stepan Gerasimov, Aug 03 2013

The primes indices k are 1, 2, 10, 24, 54, 120, 159, 214, 231, 1027, 1161, 1447, 3100, 8188, 9695, 11363 ...
The corresponding primes 2^(k - 1) + prime(k) are 3, 5, 541, 8388697,...
a(18) > 2*10^6. - Michael S. Branicky, Apr 16 2025

			29 is in the sequence because 29 = prime(10) and 2^(10 - 1) + 29 = 512 + 29 = 541 is prime.

Cf. A077375, A227126, A242944, A244913, A244916.

for i from 1 do
    p := ithprime(i) ;
    if isprime(p+2^(i-1)) then
       printf("%d,\n",p) ;
    end if;
end do: # R. J. Mathar, Jul 12 2014

p = 2; lst = {}; While[p < 730001, If[ PrimeQ[ 2^(PrimePi@ p-1) + p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst (* Robert G. Wilson v, Jul 09 2014 *)

lista(nn) = {ip = 1; forprime(p=2, nn, if (isprime(2^(ip-1)+p), print1(p, ", ")); ip++;);} \\ Michel Marcus, Jul 12 2014

a(3) - a(9) from _Olivier Gérard_, Aug 01 2013
a(10) - a(15) from Robert G. Wilson v, Aug 01 2013
a(16) from Robert G. Wilson v, Jul 09 2014
a(17) from Michael S. Branicky, Apr 14 2025

cp's OEIS Frontend

A227126 Primes prime(k) such that 2^(k+1) - prime(k) is also prime.

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