

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



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
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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(n1) + 7*a(n3)  7*a(n4) 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



