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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.
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%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