A353072 Numbers k such that nextprime(k)-k is a positive square.

1, 2, 4, 6, 7, 10, 12, 13, 16, 18, 19, 22, 25, 28, 30, 33, 36, 37, 40, 42, 43, 46, 49, 52, 55, 58, 60, 63, 66, 67, 70, 72, 75, 78, 79, 82, 85, 88, 93, 96, 97, 100, 102, 103, 106, 108, 109, 112, 118, 123, 126, 127, 130, 133, 136, 138, 140, 145, 148, 150, 153

Offset

1,2

Comments

Numbers p-1, where p is prime is a subsequence (see A006093).

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

The next prime after 7 is 11, and 11-7 = 4 a square, so 7 is in this sequence.
The next prime after 118 is 127, 127-118 = 9 is a square, so 118 is a term.

Mathematica

Select[Range[2000], NextPrime[#] - # > 0 && IntegerQ[Sqrt[NextPrime[#] - #]] &]
npsQ[n_]:=With[{c=NextPrime[n]-n}, c>0&&IntegerQ[Sqrt[c]]]; Select[Range[200], npsQ] (* Harvey P. Dale, May 05 2023 *)

Prog

(PARI) upto(n) = {my(res = List(1), q = 2, u = nextprime(n + 1)); forprime(p = 3, u, forstep(i = sqrtint(p - q), 1, -1, listput(res, p-i^2) ); q = p ); res } \\ David A. Corneth, Apr 22 2022
(PARI) isok(k) = issquare(nextprime(k+1)-k); \\ Michel Marcus, Apr 22 2022

Crossrefs

Cf. A006093, A013632, A029710.

Sequence in context: A026504 A026230 A026144 * A286047 A325426 A227090

Adjacent sequences: A353069 A353070 A353071 * A353073 A353074 A353075

Keyword

nonn

Author

Tanya Khovanova, Apr 21 2022

Status

approved