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A278580
Numbers n such that Jacobi(n,23) = 1.
4
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).
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 29 2016
STATUS
approved