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

1,2

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

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

Prog

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

Crossrefs

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

Sequence in context: A174738 A011867 A008725 * A347327 A026445 A279078

Adjacent sequences: A275670 A275671 A275672 * A275674 A275675 A275676

Keyword

nonn

Author

Peter Kagey, Aug 04 2016

Status

approved