A297180 a(n) is the smallest positive integer of length (distance from origin) n in the Cayley graph of the integers generated by all powers of 7.

1, 2, 3, 4, 11, 18, 25, 74, 123, 172, 515, 858, 1201, 3602, 6003, 8404, 25211, 42018, 58825, 176474, 294123, 411772, 1235315, 2058858, 2882401, 8647202, 14412003, 20176804, 60530411, 100884018, 141237625, 423712874, 706188123, 988663372, 2965990115, 4943316858

Offset

1,2

Links

Lars Blomberg, Table of n, a(n) for n = 1..1000

G. Bell, A. Lawson, N. Pritchard, and D. Yasaki, Locally infinite Cayley graphs of the integers, arXiv:1711.00809 [math.GT], 2017.

Formula

Conjectures from Colin Barker, Dec 28 2017: (Start)

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

a(n) = a(n-1) + 7*a(n-3) - 7*a(n-4) for n>4.

(End)

The second conjecture by Colin Barker is true up to n=1000. - Lars Blomberg, Dec 29 2017

Crossrefs

Cf. A007583, A007051, A294566, A297181, A297182 for the sequences obtained if "7" is replaced by a different prime.

Sequence in context: A192613 A002098 A301318 * A162969 A104109 A066347

Adjacent sequences: A297177 A297178 A297179 * A297181 A297182 A297183

Keyword

nonn

Author

N. J. A. Sloane, Dec 28 2017

Extensions

Terms a(21) and beyond from Lars Blomberg, Dec 29 2017

Status

approved