The On-Line Encyclopedia of Integer Sequences (OEIS)

A047406 revision #33

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..57.

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

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