A259749 Numbers that are congruent to {1,2,5,7,10,11,13,17,19,23} mod 24.

1, 2, 5, 7, 10, 11, 13, 17, 19, 23, 25, 26, 29, 31, 34, 35, 37, 41, 43, 47, 49, 50, 53, 55, 58, 59, 61, 65, 67, 71, 73, 74, 77, 79, 82, 83, 85, 89, 91, 95, 97, 98, 101, 103, 106, 107, 109, 113, 115, 119, 121, 122, 125, 127, 130, 131, 133, 137, 139, 143, 145

Offset

1,2

Comments

Original name: Numbers n such that A259748(n) = 0.

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-2,2,-1).

Formula

A259748(a(n)) = Sum_{x*y: x,y in Z/a(n)Z, x<>y} = 0.

G.f.: x*(1+x^2)*(1+2*x^2-x^3+2*x^4-2*x^5+3*x^6+x^7) / ((1-x)^2*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)). - Colin Barker, Aug 25 2016

Mathematica

A[n_] := A[n] = Sum[a b, {a, 1, n}, {b, a + 1, n}] ; Select[Range[600], Mod[A[#], #]  == 0 & ]
Rest@ CoefficientList[Series[x (1 + x^2) (1 + 2 x^2 - x^3 + 2 x^4 - 2 x^5 + 3 x^6 + x^7)/((1 - x)^2*(1 - x + x^2 - x^3 + x^4) (1 + x + x^2 + x^3 + x^4)), {x, 0, 61}], x] (* Michael De Vlieger, Aug 25 2016 *)
Select[Range[150], MemberQ[{1, 2, 5, 7, 10, 11, 13, 17, 19, 23}, Mod[#, 24]]&] (* or *) LinearRecurrence[{2, -2, 2, -2, 2, -2, 2, -2, 2, -1}, {1, 2, 5, 7, 10, 11, 13, 17, 19, 23}, 70] (* Harvey P. Dale, Jan 15 2022 *)

Prog

(PARI) Vec(x*(1+x^2)*(1+2*x^2-x^3+2*x^4-2*x^5+3*x^6+x^7)/((1-x)^2*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)) + O(x^100)) \\ Colin Barker, Aug 25 2016

Crossrefs

Cf. A000914.

Other sequences of numbers n such that A259748(n)/n equals a constant: A008606, A073762, A259750, A259751, A259752, A259754, A259755.

Sequence in context: A099477 A261034 A330777 * A067934 A284470 A112730

Adjacent sequences: A259746 A259747 A259748 * A259750 A259751 A259752

Keyword

nonn,easy

Author

José María Grau Ribas, Jul 04 2015

Extensions

Better name from Danny Rorabaugh, Oct 22 2015

Status

approved