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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A056107, A056834, A160389.

Programs

Mathematica

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

PARI

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

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)