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A329095 Odd numbers k such that x^2 == 2 (mod k) has no solution. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A325129 A173263 A285141 * A319009 A294427 A141231

Adjacent sequences:  A329092 A329093 A329094 * A329096 A329097 A329098

KEYWORD

nonn,easy

AUTHOR

Jianing Song, Nov 04 2019

STATUS

approved

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Last modified May 12 10:54 EDT 2021. Contains 343821 sequences. (Running on oeis4.)