A139401 -id:A139401 - cp's OEIS frontend

A100867 Smallest positive integer k such that A000037(n) is not a quadratic residue modulo k.

3, 4, 3, 4, 4, 3, 4, 3, 5, 5, 3, 4, 3, 4, 4, 3, 8, 4, 3, 7, 3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 5, 3, 4, 7, 3, 4, 4, 3, 7, 4, 3, 5, 3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 9, 7, 3, 4, 3, 4, 4, 3, 7, 4, 3, 5, 5, 3, 4, 7, 3, 4, 4, 3, 4, 3, 9, 8, 3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 7, 5, 3, 4, 3, 4, 4, 3, 9, 4, 3, 5, 8, 3, 4, 5, 3, 4, 4

Offset: 1

Guilherme de Queiroz Hobbs (guilhermehobbs(AT)uol.com.br), Jan 08 2005

nonn

The nonzero terms of A139401.

			a(1) = 3 because the first nonsquare positive integer is 2 and 2 is not a quadratic residue modulo 3.

a(n) = A139401(A000037(n)).

Corrected and extended by David Wasserman, Mar 04 2008

Edited by Max Alekseyev, May 11 2010

A354597 a(n) is the smallest number k>0 such that -n is not a quadratic residue modulo k.

Original entry on oeis.org

3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 7, 5, 3, 4, 7, 3, 4, 4, 3, 11, 4, 3, 5, 9, 3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 8, 7, 3, 4, 7, 3, 4, 4, 3, 7, 4, 3, 5, 5, 3, 4, 7, 3, 4, 4, 3, 11, 4, 3, 8, 7, 3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 7, 5, 3, 4, 8, 3, 4, 4, 3, 11, 4, 3, 5, 9, 3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 7, 9, 3, 4, 7, 3

Offset: 1

Bruno Langlois, Jul 08 2022

nonn

All values are prime powers, and every prime power except 2 appears in the sequence. This can be proved using the Chinese remainder theorem.

Cf. A139401.

a(n) = my(k=2); while (issquare(Mod(-n, k)), k++); k; \\ Michel Marcus, Jul 08 2022

cp's OEIS Frontend

A100867 Smallest positive integer k such that A000037(n) is not a quadratic residue modulo k.

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A354597 a(n) is the smallest number k>0 such that -n is not a quadratic residue modulo k.

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