A047406 Numbers that are congruent to {4, 6} mod 8.

4, 6, 12, 14, 20, 22, 28, 30, 36, 38, 44, 46, 52, 54, 60, 62, 68, 70, 76, 78, 84, 86, 92, 94, 100, 102, 108, 110, 116, 118, 124, 126, 132, 134, 140, 142, 148, 150, 156, 158, 164, 166, 172, 174, 180, 182, 188, 190, 196, 198, 204, 206, 212, 214, 220, 222, 228

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

In groups of four, add the odd and even numbers (4=1+3, 6=2+4; 12=5+7, 14=6+8; etc.). - George E. Antoniou, Dec 12 2001

The first 250 terms (4 through 998) are the 250 non-occurring Fibonacci number residues modulo 1000; i.e., if leading zeros are supplied as necessary for the terms having fewer than three digits, these are the 250 sets of three digits that never appear as the last three digits of a Fibonacci number. - Jon E. Schoenfield, Jul 05 2010

Examples

			a(2) = 8*2 - 4 - 6 = 6;
a(3) = 8*3 - 6 - 6 = 12;
a(4) = 8*4 - 12 - 6 = 14.
		

Links

• David Lovler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Union of A017113 and A017137.

Cf. A042964.

Programs

Mathematica

Select[Range[230], MemberQ[{4, 6}, Mod[#, 8]] &] (* Amiram Eldar, Dec 19 2021 *)

PARI

a(n)=4*n-1-(-1)^n \\ Charles R Greathouse IV, May 20 2013

Formula

a(n) = A042964(n)*2.

a(n) = (4*n - 1 - (-1)^n). - Jon E. Schoenfield, Jul 05 2010

a(n) = 8*n - a(n-1) - 6 (with a(1)=4). - Vincenzo Librandi, Aug 05 2010

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

From Wesley Ivan Hurt, May 18 2013: (Start)

a(n) = (8 * ceiling(n/2) - 4) * (n mod 2) + (8 * ceiling(n/2) - 2) * (n+1 mod 2).

a(n) = 8 * ceiling(n/2) - 3 + (-1)^n. (End)

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

E.g.f.: 2*(1 + 2*x*exp(x) - cosh(x)). - David Lovler, Sep 02 2022