A306257 a(n) = t for the minimal integer k > t such that k^2 mod n = t^2 is a perfect square.

0, 0, 1, 0, 2, 2, 2, 1, 0, 3, 3, 2, 3, 3, 1, 0, 4, 0, 4, 4, 2, 4, 4, 1, 0, 5, 3, 5, 5, 2, 5, 2, 4, 5, 1, 0, 6, 6, 5, 3, 6, 4, 6, 6, 2, 6, 6, 1, 0, 0, 7, 7, 7, 6, 3, 5, 5, 7, 7, 2, 7, 7, 1, 0, 4, 8, 8, 8, 7, 2, 8, 3, 8, 8, 5, 8, 2, 7, 8, 1, 0, 9, 9, 4, 6, 9, 7, 9, 9, 4, 3, 9, 8, 9, 7, 2, 9, 0, 1, 0, 10, 8, 10, 9, 4

Offset

1,5

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Formula

a(n) = 0 <=> n > 0 and n in { A000290 } union { A077591 }.

Maple

a:= proc(n) local k; for k from (s-> `if`(s^2<n, s+1, s))(isqrt(n))
       while not issqr(irem(k^2, n)) do od; isqrt(irem(k^2, n))
    end:
seq(a(n), n=1..120);

Crossrefs

Cf. A000290, A077591, A306271 (values of k).

Sequence in context: A176389 A076451 A230536 * A357316 A108839 A114898

Adjacent sequences: A306254 A306255 A306256 * A306258 A306259 A306260

Keyword

nonn,look

Author

Alois P. Heinz, Feb 13 2019

Status

approved