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

1,2

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,...

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A155763 A347350 A030319 * A180040 A166274 A343732

Adjacent sequences: A226378 A226379 A226380 * A226382 A226383 A226384

Keyword

nonn

Author

Gerasimov Sergey, Jun 05 2013

Extensions

Corrected by Giovanni Resta, Jun 09 2013

Status

approved