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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 14 17:32 EST 2019. Contains 329979 sequences. (Running on oeis4.)