

A275673


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


1



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
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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(n1)a(n2)+a(n6)2*a(n7)+a(n8) for n>8.
G.f.: x*(1x^6+x^7) / ((1x)^3*(1+x)*(1x+x^2)*(1+x+x^2)).
(End)
Conjecture: a(n) = (n+43*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



