|
%I #11 Dec 30 2017 03:44:04
%S 1,2,3,4,11,18,25,74,123,172,515,858,1201,3602,6003,8404,25211,42018,
%T 58825,176474,294123,411772,1235315,2058858,2882401,8647202,14412003,
%U 20176804,60530411,100884018,141237625,423712874,706188123,988663372,2965990115,4943316858
%N 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.
%H Lars Blomberg, <a href="/A297180/b297180.txt">Table of n, a(n) for n = 1..1000</a>
%H G. Bell, A. Lawson, N. Pritchard, and D. Yasaki, <a href="https://arxiv.org/abs/1711.00809">Locally infinite Cayley graphs of the integers</a>, arXiv:1711.00809 [math.GT], 2017.
%F Conjectures from _Colin Barker_, Dec 28 2017: (Start)
%F G.f.: x*(1 + x + x^2 - 6*x^3) / ((1 - x)*(1 - 7*x^3)).
%F a(n) = a(n-1) + 7*a(n-3) - 7*a(n-4) for n>4.
%F (End)
%F The second conjecture by Colin Barker is true up to n=1000. - _Lars Blomberg_, Dec 29 2017
%Y Cf. A007583, A007051, A294566, A297181, A297182 for the sequences obtained if "7" is replaced by a different prime.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Dec 28 2017
%E Terms a(21) and beyond from _Lars Blomberg_, Dec 29 2017
|
