A047546 Numbers that are congruent to {2, 3, 4, 7} mod 8.

2, 3, 4, 7, 10, 11, 12, 15, 18, 19, 20, 23, 26, 27, 28, 31, 34, 35, 36, 39, 42, 43, 44, 47, 50, 51, 52, 55, 58, 59, 60, 63, 66, 67, 68, 71, 74, 75, 76, 79, 82, 83, 84, 87, 90, 91, 92, 95, 98, 99, 100, 103, 106, 107, 108, 111, 114, 115, 116, 119, 122, 123

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A004767, A047404, A047463, A056594.

Programs

Maple

A047546:=n->(4*n-2+I^(1-n)+I^(n-1))/2: seq(A047546(n), n=1..100); # Wesley Ivan Hurt, May 20 2016

Mathematica

Table[(4n-2+I^(1-n)+I^(n-1))/2, {n, 80}] (* Wesley Ivan Hurt, May 20 2016 *)

PARI

a(n)=(n-1)\4*8+[7,2,3,4][n%4+1] \\ Charles R Greathouse IV, Jun 11 2015

Sage

[lucas_number1(n,0,1)+2*n-1 for n in range(1,56)] # Zerinvary Lajos, Jul 06 2008

Formula

a(n) = A056594(n)+2*n-1. - Zerinvary Lajos, Jul 06 2008

a(n) = A047404(n)+1. - Zerinvary Lajos, Jul 06 2008

G.f.: x*(2-x+2*x^2+x^3) / ((1+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, May 20 2016: (Start)

a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>4.

a(n) = (4*n-2+I^(1-n)+I^(n-1))/2 where I=sqrt(-1).

a(2n) = A004767(n-1) for n>0, a(2n-1) = A047463(n). (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = 3*Pi/16 - 3*log(2)/8. - Amiram Eldar, Dec 25 2021

Extensions

More terms from Wesley Ivan Hurt, May 20 2016