A070316 Numbers n such that nextprime(n^2)-n^2 (n>=1) sets a new record.

1, 3, 5, 11, 18, 23, 42, 63, 69, 102, 128, 143, 226, 254, 349, 370, 590, 757, 833, 873, 1110, 1165, 5018, 14908, 49495, 87598, 106359, 185179, 269697, 558269, 1070246, 1673629, 4292936, 43957056, 148793437, 982920306, 1569443693, 4556758439

Offset: 1

Author

Donald S. McDonald, May 11 2002

Keywords

• nonn

Examples

			nextprime(63^2) - 63^2 = 3989 - 3969 = 20, giving the terms 63 in the present sequence and 20 in A070317.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..45, Dec 29 2007

Crossrefs

Positions of record values in A053000 for n >= 1. Cf. A070317.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; d = 0; Do[m = n; a = NextPrim[n^2] - n^2; If[a > d, d = a; Print[n]], {n, 1, 10^8}]

PARI

A070316(n,show_all=0)={my(k=0,r=0);for(n=1,n,until(nextprime(k++^2)-k^2>r ,); r=nextprime(k^2)-k^2; show_all&print1(k","));k} \\ M. F. Hasler, Mar 23 2013

Extensions

Edited by N. J. A. Sloane and Robert G. Wilson v, May 11 2002

More terms from Ralf Stephan, Oct 14 2002

Further terms from Charles R Greathouse IV, Jun 16 2007

Typo in a(38) corrected by M. F. Hasler, Mar 23 2013