A329095 Odd numbers k such that x^2 == 2 (mod k) has no solution.

3, 5, 9, 11, 13, 15, 19, 21, 25, 27, 29, 33, 35, 37, 39, 43, 45, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 75, 77, 81, 83, 85, 87, 91, 93, 95, 99, 101, 105, 107, 109, 111, 115, 117, 121, 123, 125, 129, 131, 133, 135, 139, 141, 143, 145, 147, 149, 153, 155, 157, 159, 163

Offset

1,1

Comments

Complement of A058529 over the odd numbers: odd numbers k such that x^2 == 2 (mod k) has solutions.

Odd numbers k such that at least one prime factor of k is congruent to 3 or 5 modulo 8 (at least one prime factor is in A003629).

Also odd terms in A025020.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

x^2 == 2 (mod 45) has no solution, so 45 is a term.

Maple

filter:= proc(t) (numtheory:-factorset(t) mod 8) intersect {3, 5} <> {} end proc:
select(filter, [seq(i, i=1..1000, 2)]); # Robert Israel, Nov 05 2019

Mathematica

Reap[Do[If[AnyTrue[FactorInteger[k][[All, 1]], MatchQ[Mod[#, 8], 3|5]&], Sow[k]], {k, 1, 999, 2}]][[2, 1]] (* Jean-François Alcover, Aug 22 2020 *)

Prog

(PARI) isA329095(k) = (k%2) && !issquare(Mod(2, k))

Crossrefs

Cf. A003629. A047621 is a subsequence.

Cf. A058529, A057126, A025020 (numbers k such that x^2 == 2 (mod k) has no solution).

Sequence in context: A368603 A173263 A285141 * A319009 A294427 A141231

Adjacent sequences: A329092 A329093 A329094 * A329096 A329097 A329098

Keyword

nonn,easy

Author

Jianing Song, Nov 04 2019

Status

approved