A047341 Numbers that are congruent to {3, 4} mod 7.

3, 4, 10, 11, 17, 18, 24, 25, 31, 32, 38, 39, 45, 46, 52, 53, 59, 60, 66, 67, 73, 74, 80, 81, 87, 88, 94, 95, 101, 102, 108, 109, 115, 116, 122, 123, 129, 130, 136, 137, 143, 144, 150, 151, 157, 158, 164, 165, 171

Offset

1,1

Comments

Numbers m such that m^2 == 2 (mod 7). - Vincenzo Librandi, Aug 05 2010

Numbers k such that A056107(k)/7 is an integer. - Bruno Berselli, Feb 14 2017

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

a(n)^2 = 7*A056834(a(n)) + 2. - Bruno Berselli, Nov 28 2010

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

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi*tan(Pi/14)/7. - Amiram Eldar, Dec 12 2021

E.g.f.: 3 + ((14*x - 7)*exp(x) - 5*exp(-x))/4. - David Lovler, Sep 01 2022

From Amiram Eldar, Nov 22 2024: (Start)

Product_{n>=1} (1 - (-1)^n/a(n)) = 1.

Product_{n>=1} (1 + (-1)^n/a(n)) = 2*cos(Pi/7) - 1 (A160389 - 1). (End)

Mathematica

LinearRecurrence[{1, 1, -1}, {3, 4, 10}, 50] (* Amiram Eldar, Dec 12 2021 *)

Prog

(PARI) a(n) = (14*n-5*(-1)^n-7)/4 \\ Charles R Greathouse IV, Jun 11 2015

Crossrefs

Cf. A056107, A056834, A160389.

Sequence in context: A196101 A200816 A327300 * A091910 A131179 A079353

Adjacent sequences: A047338 A047339 A047340 * A047342 A047343 A047344

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved