A047341 - OEIS

%I #50 Nov 22 2024 06:27:23

%S 3,4,10,11,17,18,24,25,31,32,38,39,45,46,52,53,59,60,66,67,73,74,80,

%T 81,87,88,94,95,101,102,108,109,115,116,122,123,129,130,136,137,143,

%U 144,150,151,157,158,164,165,171

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

%C Numbers m such that m^2 == 2 (mod 7). - _Vincenzo Librandi_, Aug 05 2010

%C Numbers k such that A056107(k)/7 is an integer. - _Bruno Berselli_, Feb 14 2017

%H David Lovler, <a href="/A047341/b047341.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n)^2 = 7*A056834(a(n)) + 2. - _Bruno Berselli_, Nov 28 2010

%F G.f.: x*(3 + x + 3*x^2)/((1 + x)*(1 - x)^2). - _R. J. Mathar_, Oct 08 2011

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

%F E.g.f.: 3 + ((14*x - 7)*exp(x) - 5*exp(-x))/4. - _David Lovler_, Sep 01 2022

%F From _Amiram Eldar_, Nov 22 2024: (Start)

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

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

%t LinearRecurrence[{1, 1, -1}, {3, 4, 10}, 50] (* _Amiram Eldar_, Dec 12 2021 *)

%o (PARI) a(n) = (14*n-5*(-1)^n-7)/4 \\ _Charles R Greathouse IV_, Jun 11 2015

%Y Cf. A056107, A056834, A160389.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_