A047385 Numbers that are congruent to {2, 5} mod 7.

2, 5, 9, 12, 16, 19, 23, 26, 30, 33, 37, 40, 44, 47, 51, 54, 58, 61, 65, 68, 72, 75, 79, 82, 86, 89, 93, 96, 100, 103, 107, 110, 114, 117, 121, 124, 128, 131, 135, 138, 142, 145, 149, 152, 156, 159, 163, 166, 170

Offset

1,1

Comments

Also, numbers n such that (n^2+3)/7 is a nonnegative integer. - Bruno Berselli, Jan 16 2016

Links

David Lovler, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(2 + 3*x + 2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011

a(n) = (14*n - (-1)^n - 7)/4. - Bruno Berselli, Dec 05 2011

a(n) = 4*n - 2 - floor(n/2). - Wesley Ivan Hurt, Oct 16 2013

E.g.f.: 2 + ((14*x - 7)*exp(x) - exp(-x))/4. - David Lovler, Sep 01 2022

From Amiram Eldar, Sep 26 2022: (Start)

a(n) = A113804(n)/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(3*Pi/14)*Pi/7. (End)

From Amiram Eldar, Nov 22 2024: (Start)

Product_{n>=1} (1 - (-1)^n/a(n)) = 2*sin(3*Pi/14) (A255249).

Product_{n>=1} (1 + (-1)^n/a(n)) = 1/(2*cos(Pi/7)) (A255240). (End)

Maple

A047385:=n->4*n-2-floor(n/2); seq(A047385(k), k=1..100); # Wesley Ivan Hurt, Oct 16 2013

Mathematica

Table[4 n - 2 - Floor[n/2], {n, 100}] (* Wesley Ivan Hurt, Oct 16 2013 *)
#+{2, 5}&/@(7*Range[0, 30])//Flatten (* Harvey P. Dale, Jul 15 2017 *)

Prog

(PARI) a(n)=(14*n-6)>>2 \\ Charles R Greathouse IV, Dec 05 2011

Crossrefs

Cf. A113804, A255240, A255249.

Sequence in context: A184922 A189461 A190506 * A284624 A086814 A211274

Adjacent sequences: A047382 A047383 A047384 * A047386 A047387 A047388

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved