cp's OEIS Frontend

A275673 List of numbers that are in a spoke of a hexagonal spiral.

%I A275673 #28 Jun 08 2017 18:53:52
%S A275673 1,2,3,4,5,6,7,9,11,13,15,17,19,22,25,28,31,34,37,41,45,49,53,57,61,
%T A275673 66,71,76,81,86,91,97,103,109,115,121,127,134,141,148,155,162,169,177,
%U A275673 185,193,201,209,217,226,235,244,253,262,271,281,291,301,311,321
%N A275673 List of numbers that are in a spoke of a hexagonal spiral.
%C A275673 This sequence contains k if and only if k is in one of the following sequences: A056105, A056106, A056107, A056108, A056109, A003215.
%C A275673 Alternatively, this sequence consists of the numbers of the form 3k^2 + bk + 1 for nonnegative k and -2 <= b <= 3.
%H A275673 Peter Kagey, <a href="/A275673/b275673.txt">Table of n, a(n) for n = 1..10003</a>
%F A275673 Conjectures from _Colin Barker_, Aug 05 2016: (Start)
%F A275673 a(n) = 2*a(n-1)-a(n-2)+a(n-6)-2*a(n-7)+a(n-8) for n>8.
%F A275673 G.f.: x*(1-x^6+x^7) / ((1-x)^3*(1+x)*(1-x+x^2)*(1+x+x^2)).
%F A275673 (End)
%F A275673 Conjecture: a(n) = (n+4-3*floor((n+4)/6)-2)*floor((n+4)/6)+1. - _Luce ETIENNE_, May 25 2017
%o A275673 (Haskell)
%o A275673 a275673 n = a275673_list !! (n - 1)
%o A275673 a275673_list = scanl (+) 1 $ concatMap (replicate 6) [1..]
%Y A275673 Cf. A056105, A056106, A056107, A056108, A056109, A003215.
%K A275673 nonn
%O A275673 1,2
%A A275673 _Peter Kagey_, Aug 04 2016