A146507 Numbers congruent to {1, 13} mod 42.

1, 13, 43, 55, 85, 97, 127, 139, 169, 181, 211, 223, 253, 265, 295, 307, 337, 349, 379, 391, 421, 433, 463, 475, 505, 517, 547, 559, 589, 601, 631, 643, 673, 685, 715, 727, 757, 769, 799, 811, 841, 853, 883, 895, 925, 937, 967, 979

Offset: 1

Author

Artur Jasinski, Oct 30 2008

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A146509, A146510, A146511, A146512.

Programs

Mathematica

Select[Range[1000],MemberQ[{1,13},Mod[#,42]]&]  (* Ray Chandler, Dec 06 2016 *)
LinearRecurrence[{1,1,-1},{1,13,43},50] (* Harvey P. Dale, Apr 15 2020 *)

Formula

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

G.f.: x*(1 + 12*x + 29*x^2)/((1 - x)^2*(1 + x)). - Ilya Gutkovskiy, Dec 06 2016

E.g.f.: 29 + ((42*x - 49)*exp(x) - 9*exp(-x))/2. - David Lovler, Sep 10 2022

Extensions

Description, formula and crossrefs corrected by Ray Chandler, Dec 06 2016