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

1,2

Links

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

Example

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

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}]

Prog

(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

Crossrefs

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

Sequence in context: A270778 A267030 A128949 * A298121 A244473 A023597

Adjacent sequences: A070313 A070314 A070315 * A070317 A070318 A070319

Keyword

nonn

Author

Donald S. McDonald, May 11 2002

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

Status

approved