A065988 a(n) is the largest prime p < n such that n mod p is a perfect square; a(n) = 0 if no such prime exists.

0, 0, 2, 3, 2, 5, 3, 7, 5, 5, 7, 11, 3, 13, 11, 5, 13, 17, 5, 19, 17, 13, 19, 23, 7, 17, 23, 19, 7, 29, 11, 31, 29, 17, 31, 7, 11, 37, 23, 31, 37, 41, 17, 43, 41, 37, 43, 47, 7, 41, 47, 43, 37, 53, 23, 47, 53, 29, 43, 59, 19, 61, 59, 11, 61, 41, 29, 67, 53, 61, 67, 71, 37, 73, 71

Offset

1,3

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Mathematica

lp[n_]:=Module[{p=Prime[PrimePi[n]]}, p=If[p==n, NextPrime[p, -1], p]; While[ !IntegerQ[ Sqrt[Mod[n, p]]], p=NextPrime[p, -1]]; p]; Join[{0, 0}, Array[lp, 80, 3]] (* Harvey P. Dale, Apr 23 2022 *)

Prog

(PARI) { for (n=1, 1000, p=precprime(n - 1);; while (p > 0 && !issquare(n%p), p=precprime(p - 1)); write("b065988.txt", n, " ", p) ) } \\ Harry J. Smith, Nov 05 2009

Crossrefs

Sequence in context: A079311 A364391 A060474 * A335285 A336268 A075105

Adjacent sequences: A065985 A065986 A065987 * A065989 A065990 A065991

Keyword

nonn

Author

Reinhard Zumkeller, Dec 10 2001

Status

approved