A113763 Non-multiples of 13, or numbers not divisible by 13.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset

1,2

Comments

Complement of A008595. - Reinhard Zumkeller, Apr 26 2011

Links

Table of n, a(n) for n=1..72.

Eric Weisstein's World of Mathematics, Triskaidekaphobia.

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

Formula

a(n) = n+floor((2*n-1)/24) = n+quotient(2*n-1, 24).

G.f.: x*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12) / ( (1+x)*(1+x^2)*(x^4-x^2+1)*(x^2-x+1)*(1+x+x^2)*(x-1)^2 ). - R. J. Mathar, May 25 2026

Mathematica

Table[n+Quotient[2n-1, 24], {n, 1, 85}]; (* or *)Table[n+Floor[(2n-1)/24], {n, 1, 85}]

Prog

(SageMath) [i for i in range(80) if not i%13] # Zerinvary Lajos, Apr 21 2009
(PARI) a(n)=(26*n-1)\24 \\ Charles R Greathouse IV, Jun 08 2015

Crossrefs

Cf. A011760, A023806.

Sequence in context: A391732 A172270 A023806 * A322847 A302492 A023754

Adjacent sequences: A113760 A113761 A113762 * A113764 A113765 A113766

Keyword

nonn,easy

Author

Zak Seidov, Jan 18 2006

Status

approved