A076948 Smallest k such that nk-1 is a square, or 0 if no such number exists.

1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 10, 0, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 10, 13, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 1, 0

Offset: 1

Author

Amarnath Murthy, Oct 20 2002

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008784.

Cf. A037213.

Programs

Haskell

a076948 1 = 1
a076948 n = if null qs then 0 else head qs
            where qs = filter ((> 0) . a037213 . subtract 1 . (* n)) [1..n]
-- Reinhard Zumkeller, Oct 25 2015

Mathematica

a[n_] := Module[{r, j, k}, r = Solve[j>0 && k>0 && n k - 1 == j^2, {j, k}, Integers]; If[r === {}, Return[0], Return[k /. (r /. C[1] -> 0) // Min]]]; a[1] = 1;
Array[a, 100] (* Jean-François Alcover, Apr 27 2020 *)

PARI

a(n) = if (!issquare(Mod(-1, n)), 0, my(k=1); while (!issquare(n*k-1), k++); k); \\ Michel Marcus, Apr 27 2020

Formula

a(n) != 0 if and only if n is a term of A008784. - Joerg Arndt, Apr 27 2020

a(n) = 1 if and only if n is a term of A002522. - Bernard Schott, Apr 27 2020

Extensions

Edited and extended by Robert G. Wilson v, Oct 21 2002