%I #7 Jun 27 2013 17:31:13
%S 1,2,5,7,10,18,52,83,113,133,169,226,347,568,909,4612,8014
%N Numbers n such that the distance from 2^(2n) to the prev prime is the same as the distance from (2n)^2 to the prev prime.
%C Numbers n such that 2^(2n) - (largest prime < 2^(2n)) = (2n)^2 -(largest prime < (2n)^2).
%C Primes in the sequence are: 2, 5, 7,...
%e 1 is in the sequence because the distance from 4 to 3 is the same as the distance from 4 to 3.
%e 2 is in the sequence because the distance from 16 to 13 is the same as the distance from 16 to 13.
%e 5 is in the sequence because the distance from 1024 to 1021 is the same as the distance from 100 to 97.
%t dP[x_] := x - NextPrime[x, -1]; Select[Range[250]*2, (d = dP[#^2]; PrimeQ[2^# - d] && d == dP[2^#]) &]/2 (* _Giovanni Resta_, Jun 14 2013 *)
%Y Cf. A226381.
%K nonn,less
%O 1,2
%A _Gerasimov Sergey_, Jun 14 2013
%E a(7)-a(17) from _Giovanni Resta_, Jun 14 2013