A047608 Numbers that are congruent to {4, 5} mod 8.

4, 5, 12, 13, 20, 21, 28, 29, 36, 37, 44, 45, 52, 53, 60, 61, 68, 69, 76, 77, 84, 85, 92, 93, 100, 101, 108, 109, 116, 117, 124, 125, 132, 133, 140, 141, 148, 149, 156, 157, 164, 165, 172, 173, 180, 181, 188, 189, 196, 197, 204, 205, 212, 213, 220, 221, 228, 229

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• David Lovler, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Union of A017113 and A004770.

Programs

Mathematica

Select[Range[230], MemberQ[{4, 5}, Mod[#, 8]] &] (* Amiram Eldar, Dec 19 2021 *)

PARI

a(n) = 4*n - 3*(1 + (-1)^n)/2 \\ David Lovler, Aug 20 2022

Formula

G.f.: x*(4+x+3*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Sep 22 2016

a(n) = 4n - 3*(1 + (-1)^n)/2 or a(n) = 4n - 3*((n-1) mod 2). - Heinz Ebert, Jul 12 2021

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)-1)*Pi/16 - log(2)/4 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 19 2021

E.g.f.: 3 + ((8*x - 3)*exp(x) - 3*exp(-x))/2. - David Lovler, Aug 20 2022