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

1,1

Links

Table of n, a(n) for n=1..62.

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

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

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 *)

Prog

(Sage) [lucas_number1(n, 0, 1)+2*n-1 for n in range(1, 56)] # Zerinvary Lajos, Jul 06 2008
(PARI) a(n)=(n-1)\4*8+[7, 2, 3, 4][n%4+1] \\ Charles R Greathouse IV, Jun 11 2015

Crossrefs

Cf. A004767, A047404, A047463, A056594.

Sequence in context: A080724 A342780 A089589 * A266530 A266510 A266540

Adjacent sequences: A047543 A047544 A047545 * A047547 A047548 A047549

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 20 2016

Status

approved