A226650 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.

1, 2, 5, 7, 10, 18, 52, 83, 113, 133, 169, 226, 347, 568, 909, 4612, 8014

Offset

1,2

Comments

Numbers n such that 2^(2n) - (largest prime < 2^(2n)) = (2n)^2 -(largest prime < (2n)^2).

Primes in the sequence are: 2, 5, 7,...

Links

Table of n, a(n) for n=1..17.

Example

1 is in the sequence because the distance from 4 to 3 is the same as the distance from 4 to 3.
2 is in the sequence because the distance from 16 to 13 is the same as the distance from 16 to 13.
5 is in the sequence because the distance from 1024 to 1021 is the same as the distance from 100 to 97.

Mathematica

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 *)

Crossrefs

Cf. A226381.

Sequence in context: A355846 A362388 A076802 * A024374 A297103 A065219

Adjacent sequences: A226647 A226648 A226649 * A226651 A226652 A226653

Keyword

nonn,less

Author

Gerasimov Sergey, Jun 14 2013

Extensions

a(7)-a(17) from Giovanni Resta, Jun 14 2013

Status

approved