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

1,13

Links

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

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

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 *)

Prog

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

Crossrefs

Cf. A008784.

Cf. A037213.

Sequence in context: A357879 A072325 A294929 * A255309 A335446 A335460

Adjacent sequences: A076945 A076946 A076947 * A076949 A076950 A076951

Keyword

nonn

Author

Amarnath Murthy, Oct 20 2002

Extensions

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

Status

approved