A047425 Numbers that are congruent to {3, 4, 5, 6} mod 8.

3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21, 22, 27, 28, 29, 30, 35, 36, 37, 38, 43, 44, 45, 46, 51, 52, 53, 54, 59, 60, 61, 62, 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85, 86, 91, 92, 93, 94, 99, 100, 101, 102, 107, 108, 109, 110, 115, 116, 117, 118, 123, 124

Offset

1,1

Comments

Complement of numbers congruent to {0, 1, 2, 7} mod 8. - Jaroslav Krizek, Dec 19 2009

In general, sequences congruent to {a, a + i, a + 2i, ..., a + pi} mod k and a + p*i < k have a general form of (k - i*p)*floor(n/p) + i*n + a, from offset 0. - Gary Detlefs, Oct 20 2013

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

G.f.: x*(3+x+x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

a(n) = 8*floor((n-1)/4) + ((n-1) mod 4) + 3.

a(n) = OR(n-1, 1) + OR(n-1, 2). - Gary Detlefs, Oct 20 2013

From Wesley Ivan Hurt, May 31 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

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

a(2k) = A047406(k), a(2k-1) = A047621(k). (End)

E.g.f.: 2 + sin(x) - cos(x) + 2*x*sinh(x) + (2*x - 1)*cosh(x). - Ilya Gutkovskiy, May 31 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/16 + (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2-sqrt(2))/4. - Amiram Eldar, Dec 26 2021

Maple

A047425:=n->8*floor((n-1)/4)+((n-1) mod 4)+3: seq(A047425(n), n=1..100); # Wesley Ivan Hurt, May 31 2016

Mathematica

Flatten[# + {3, 4, 5, 6} &/@(8*Range[0, 15])] (* Harvey P. Dale, Jun 26 2011 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [3, 4, 5, 6]]; // Wesley Ivan Hurt, May 31 2016

Crossrefs

Cf. A047406, A047621.

Sequence in context: A261459 A215249 A089912 * A048989 A356050 A299299

Adjacent sequences: A047422 A047423 A047424 * A047426 A047427 A047428

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved