A226381 Numbers n such that the distance from n to the next prime is the same as the distance from n^2 to the next prime.

1, 2, 3, 4, 6, 7, 8, 9, 10, 13, 15, 16, 21, 31, 36, 37, 38, 39, 40, 45, 48, 50, 57, 61, 64, 66, 67, 76, 81, 85, 91, 97, 99, 103, 105, 111, 126, 130, 131, 141, 147, 150, 151, 154, 156, 163, 168, 171, 180, 181, 185, 193, 202, 207, 210, 216, 225, 235, 237, 240, 246, 248, 249, 250, 253

Offset: 1

Author

Gerasimov Sergey, Jun 05 2013

Keywords

• nonn

Comments

Numbers n such that (smallest prime > n)- n = (smallest prime > n^2)- n^2.

Primes in the sequence are: 2, 3, 7, 13, 31, 37, 61, 67, 97, 103, 131, 151, 163, 181, 193,...

Examples

			1 is in the sequence because the distance from 1 to 2 is the same as the distance from 1^2 to 2.
2 is in the sequence because the distance from 2 to 3 is the same as the distance from 2^2 to 5.
3 is in the sequence because the distance from 3 to 5 is the same as the distance from 3^2 to 11.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Select[Range[235], NextPrime[#] - # == NextPrime[#^2] - #^2 &] (* Giovanni Resta, Jun 09 2013 *)

PARI

is(n)=nextprime(n+1)-n==nextprime(n^2)-n^2 \\ Charles R Greathouse IV, Jun 14 2013

Formula

{n: A013632(n) = A013632(n^2)}. - R. J. Mathar, Jun 09 2013

Extensions

Corrected by Giovanni Resta, Jun 09 2013