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

Author

N. J. A. Sloane, Nov 29 2016

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A010385, A000594, A063987, A278579.

Programs

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 *)

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

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)