A297181 - OEIS

%I #12 Dec 30 2017 03:43:58

%S 1,2,3,4,5,6,17,28,39,50,61,182,303,424,545,666,1997,3328,4659,5990,

%T 7321,21962,36603,51244,65885,80526,241577,402628,563679,724730,

%U 885781,2657342,4428903,6200464,7972025,9743586,29230757,48717928,68205099,87692270

%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 11.

%H Lars Blomberg, <a href="/A297181/b297181.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 + x^3 + x^4 - 10*x^5) / ((1 - x)*(1 - 11*x^5)).

%F a(n) = a(n-1) + 11*a(n-5) - 11*a(n-6) for n>5.

%F (End)

%F The second conjecture by Colin Barker is true up to n=1000. - _Lars Blomberg_, Dec 29 2017

%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