A278580 - OEIS

%I #15 Jun 25 2020 19:20:32

%S 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,

%T 50,52,54,55,58,59,62,64,70,71,72,73,75,77,78,81,82,85,87,93,94,95,96,

%U 98,100,101,104,105,108,110,116,117,118,119,121,123,124,127,128,131,133,139,140,141,142,144,146

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

%C Important for the study of Ramanujan numbers A000594.

%C 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).

%H Colin Barker, <a href="/A278580/b278580.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,1,-1).

%F From _Colin Barker_, Nov 30 2016: (Start)

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

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

%F 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))

%F (End)

%t 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 *)

%o (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

%Y Cf. A010385, A000594, A063987, A278579.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Nov 29 2016