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%I #50 Mar 07 2024 11:13:06
%S 2,3,5,11,17,167,193,197,433,4111,9173,42929,95279,98897,139409,
%T 142567,228617,329333,344209,791191,829177
%N Primes p_i such that 2^(i+1) - p_i is also prime.
%C The corresponding primes 2^(i + 1) - prime(i) are 2, 5, 11, 53, 239, 1099511627609, 35184372088639, ...
%C The prime indices i are 1, 2, 3, 5, 7, 39, 44, 45, 84, 566, 1137, ...
%e 5 is a term because 5 is the 3rd prime, and 2^(3+1) - 5 = 16 - 5 = 11 which is a prime
%e 11 is in the sequence because 11 = prime(5) and 2^(5 + 1) - 11 = 64 - 11 = 53 is a prime.
%t 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 *)
%o (PARI) lista(nn) = {ip = 1; forprime(p=2, nn, if (isprime(2^(ip+1)-p), print1(p, ", ")); ip++;);} \\ _Michel Marcus_, Jul 12 2014
%Y Cf. A078686, A244913.
%K nonn,more
%O 1,1
%A _Gerasimov Sergey_, Jul 02 2013
%E a(3), a(6), a(8)- a(12) from _Joerg Arndt_, Jul 03 2013
%E Corrected and extended through a(21) by _Robert G. Wilson v_, Jul 09 2014
%E Entry revised by _N. J. A. Sloane_, Jan 02 2019, incorporating data from a later submission from _Robert G. Wilson v_
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