A146507 - OEIS

%I #22 Sep 11 2022 09:34:49

%S 1,13,43,55,85,97,127,139,169,181,211,223,253,265,295,307,337,349,379,

%T 391,421,433,463,475,505,517,547,559,589,601,631,643,673,685,715,727,

%U 757,769,799,811,841,853,883,895,925,937,967,979

%N Numbers congruent to {1, 13} mod 42.

%C Positive integers k such that Hypergeometric[k/14,(14-k)/14,1/2,3/4] = 2*cos(2Pi/7).

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

%F a(2k-1) = 42*(k-1)+1, a(2k) = 42*(k-1)+13, where k>0.

%F G.f.: x*(1 + 12*x + 29*x^2)/((1 - x)^2*(1 + x)). - _Ilya Gutkovskiy_, Dec 06 2016

%F E.g.f.: 29 + ((42*x - 49)*exp(x) - 9*exp(-x))/2. - _David Lovler_, Sep 10 2022

%t Select[Range[1000],MemberQ[{1,13},Mod[#,42]]&]  (* _Ray Chandler_, Dec 06 2016 *)

%t LinearRecurrence[{1,1,-1},{1,13,43},50] (* _Harvey P. Dale_, Apr 15 2020 *)

%Y Cf. A146509, A146510, A146511, A146512.

%K nonn

%O 1,2

%A _Artur Jasinski_, Oct 30 2008

%E Description, formula and crossrefs corrected by _Ray Chandler_, Dec 06 2016