A278580 Numbers n such that Jacobi(n,23) = 1.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 25, 26, 27, 29, 31, 32, 35, 36, 39, 41, 47, 48, 49, 50, 52, 54, 55, 58, 59, 62, 64, 70, 71, 72, 73, 75, 77, 78, 81, 82, 85, 87, 93, 94, 95, 96, 98, 100, 101, 104, 105, 108, 110, 116, 117, 118, 119, 121, 123, 124, 127, 128, 131, 133, 139, 140, 141, 142, 144, 146

Offset

1,2

Comments

Important for the study of Ramanujan numbers A000594.

The first 11 terms, 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, are the quadratic residues mod 23 (see row 23 of A063987).

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,1,-1).

Formula

From Colin Barker, Nov 30 2016: (Start)

a(n+11) = a(n) + 23.

a(n) = a(n-1) + a(n-11) - a(n-12) for n>12.

G.f.: x*(1 +x +x^2 +x^3 +2*x^4 +2*x^5 +x^6 +3*x^7 +x^8 +3*x^9 +2*x^10 +5*x^11) / ((1 -x)^2*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6 +x^7 +x^8 +x^9 +x^10))

(End)

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24}, 90] (* Harvey P. Dale, Jun 25 2020 *)

Prog

(PARI) Vec(x*(1+x+x^2+x^3+2*x^4+2*x^5+x^6+3*x^7+x^8+3*x^9+2*x^10+5*x^11) / ((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)) + O(x^100)) \\ Colin Barker, Nov 30 2016

Crossrefs

Cf. A010385, A000594, A063987, A278579.

Sequence in context: A071403 A010407 A035240 * A028929 A308299 A356940

Adjacent sequences: A278577 A278578 A278579 * A278581 A278582 A278583

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 29 2016

Status

approved