

A330404


Least nonsquare k that is a quadratic residue modulo n.


2



2, 2, 3, 5, 5, 3, 2, 8, 7, 5, 3, 12, 3, 2, 6, 17, 2, 7, 5, 5, 7, 3, 2, 12, 6, 3, 7, 8, 5, 6, 2, 17, 3, 2, 11, 13, 3, 5, 3, 20, 2, 7, 6, 5, 10, 2, 2, 33, 2, 6, 13, 12, 6, 7, 5, 8, 6, 5, 3, 21, 3, 2, 7, 17, 10, 3, 6, 8, 3, 11, 2, 28, 2, 3, 6, 5, 11, 3, 2, 20, 7, 2, 3, 21
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OFFSET

1,1


COMMENTS

a(n) >= n if and only if n is in A254328.
It seems that lim_{n>oo} a(n)/n = 0. Conjectured last term m such that a(m)/m >= 1/k, k = 1, 2, 3, ...: 16, 48, 240, 288, 720, 720, 720, 720, 1008, 1440, ...


LINKS

Jianing Song, Table of n, a(n) for n = 1..10000


EXAMPLE

k is a quadratic residue modulo 16 if and only if k == 0, 1, 4, 9 (mod 16). Since 0, 1, 4, 9 and 16 are squares, a(16) = 17.
k is a quadratic residue modulo 48 if and only if k == 0, 1, 4, 9, 16, 25, 33, 36 (mod 48). Since 0, 1, 4, 9, 16 and 25 are squares, a(48) = 33.
k is a quadratic residue modulo 720 if and only if k == 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 145, ..., 676 (mod 720). Since 0, 1, 4, ..., 144 are squares, a(720) = 145.


PROG

(PARI) a(n) = my(k=1); while(!issquare(Mod(k, n))  issquare(k), k++); k


CROSSREFS

Cf. A254328, A330423.
Sequence in context: A174094 A284114 A323480 * A139171 A329570 A279724
Adjacent sequences: A330401 A330402 A330403 * A330406 A330407 A330408


KEYWORD

nonn


AUTHOR

Jianing Song, Dec 14 2019


STATUS

approved



