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

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, 66, 71, 76, 81, 86, 91, 97, 103, 109, 115, 121, 127, 134, 141, 148, 155, 162, 169, 177, 185, 193, 201, 209, 217, 226, 235, 244, 253, 262, 271, 281, 291, 301, 311, 321

Offset: 1

Author

Peter Kagey, Aug 04 2016

Keywords

• nonn

Comments

This sequence contains k if and only if k is in one of the following sequences: A056105, A056106, A056107, A056108, A056109, A003215.

Alternatively, this sequence consists of the numbers of the form 3k^2 + bk + 1 for nonnegative k and -2 <= b <= 3.

Links

• Peter Kagey, Table of n, a(n) for n = 1..10003

Crossrefs

Cf. A056105, A056106, A056107, A056108, A056109, A003215.

Programs

Haskell

a275673 n = a275673_list !! (n - 1)
a275673_list = scanl (+) 1 $ concatMap (replicate 6) [1..]

Formula

Conjectures from Colin Barker, Aug 05 2016: (Start)

a(n) = 2*a(n-1)-a(n-2)+a(n-6)-2*a(n-7)+a(n-8) for n>8.

G.f.: x*(1-x^6+x^7) / ((1-x)^3*(1+x)*(1-x+x^2)*(1+x+x^2)).

(End)

Conjecture: a(n) = (n+4-3*floor((n+4)/6)-2)*floor((n+4)/6)+1. - Luce ETIENNE, May 25 2017