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

1,2

Comments

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

Links

Table of n, a(n) for n=1..48.

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

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

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 *)

Crossrefs

Cf. A146509, A146510, A146511, A146512.

Sequence in context: A136191 A268483 A039318 * A113831 A139494 A043141

Adjacent sequences: A146504 A146505 A146506 * A146508 A146509 A146510

Keyword

nonn

Author

Artur Jasinski, Oct 30 2008

Extensions

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

Status

approved