A047457 Numbers that are congruent to {3, 4} mod 8.

3, 4, 11, 12, 19, 20, 27, 28, 35, 36, 43, 44, 51, 52, 59, 60, 67, 68, 75, 76, 83, 84, 91, 92, 99, 100, 107, 108, 115, 116, 123, 124, 131, 132, 139, 140, 147, 148, 155, 156, 163, 164, 171, 172, 179, 180, 187, 188, 195, 196, 203, 204, 211, 212, 219, 220, 227

Offset

1,1

Comments

Union of A017101 and A017113. - Michel Marcus, Feb 25 2014

Numbers whose binary reflected Gray code (A014550) has a single trailing zero. - Amiram Eldar, May 17 2021

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) = 8*n - a(n-1) - 9 (with a(1) = 3). - Vincenzo Librandi, Aug 06 2010

G.f.: x*(3+x+4*x^2)/((1-x)^2*(1+x)). - Colin Barker, May 13 2012

a(n) = (-5 - 3*(-1)^n + 8*n)/2. - Colin Barker, May 14 2012

A000120(a(n)-1) = A000120(a(n)+1) = A063787(n). - Ilya Lopatin and Juri-Stepan Gerasimov, Feb 25 2014

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 18 2021

Maple

A047457:=n->(-5 - 3*(-1)^n + 8*n)/2; seq(A047457(n), n=1..100); # Wesley Ivan Hurt, Mar 04 2014

Mathematica

Table[(-5 - 3*(-1)^n + 8*n)/2, {n, 100}] (* Wesley Ivan Hurt, Mar 04 2014 *)
Flatten[Table[8n + {3, 4}, {n, 0, 29}]] (* Alonso del Arte, Mar 04 2014 *)

Crossrefs

Cf. A000120, A014550, A017101, A017113, A047456 (superset), A063787.

Sequence in context: A244005 A228236 A344346 * A226632 A098377 A075646

Adjacent sequences: A047454 A047455 A047456 * A047458 A047459 A047460

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved