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A318911
Numbers k such that -3 is a quadratic residue modulo 360*k + 1, 360*k + 2, 360*k + 3 and 360*k + 4.
2
0, 2, 13, 17, 18, 20, 21, 25, 31, 40, 47, 51, 54, 57, 68, 69, 76, 83, 91, 102, 109, 110, 117, 119, 120, 131, 132, 134, 138, 142, 145, 149, 168, 171, 174, 176, 179, 182, 183, 189, 204, 205, 207, 208, 211, 212, 218, 229, 230, 234, 245, 253, 263, 281, 286, 293, 295
OFFSET
1,2
COMMENTS
Companion sequence to A318527, as it is shown there that all terms in A318527 are congruent to 1 mod 360.
Also numbers k such that -3 is a quadratic residue modulo (360*k + 1)*(360*k + 2)*(360*k + 3)*(360*k + 4)/2.
The number of terms <= 1000, 10000 and 100000 are 156, 1100 and 8056, respectively. There are also 22 pairs of consecutive numbers <= 1000, 99 pairs <= 10000 and 540 pairs <= 100000.
FORMULA
a(n) = (A318527(n) - 1)/360.
EXAMPLE
2 is a term since 93^2 == -3 (mod 721), 137^2 == -3 (mod 722), 210^2 == -3 (mod 723) and 97^2 == -3 (mod 724).
PROG
(PARI) isA057128(n) = issquare(Mod(-3, n));
isA318911(n) = isA057128(360*n+1) && isA057128(360*n+2) && isA057128(360*n+3) && isA057128(360*n+4);
CROSSREFS
Cf. A318527.
Sequence in context: A298295 A257636 A258317 * A065245 A158845 A163786
KEYWORD
nonn
AUTHOR
Jianing Song, Sep 05 2018
STATUS
approved