login
A297181
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.
2
1, 2, 3, 4, 5, 6, 17, 28, 39, 50, 61, 182, 303, 424, 545, 666, 1997, 3328, 4659, 5990, 7321, 21962, 36603, 51244, 65885, 80526, 241577, 402628, 563679, 724730, 885781, 2657342, 4428903, 6200464, 7972025, 9743586, 29230757, 48717928, 68205099, 87692270
OFFSET
1,2
LINKS
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 + x^3 + x^4 - 10*x^5) / ((1 - x)*(1 - 11*x^5)).
a(n) = a(n-1) + 11*a(n-5) - 11*a(n-6) for n>5.
(End)
The second conjecture by Colin Barker is true up to n=1000. - Lars Blomberg, Dec 29 2017
CROSSREFS
Sequence in context: A115896 A116018 A337865 * A294121 A048095 A264975
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 28 2017
EXTENSIONS
Terms a(21) and beyond from Lars Blomberg, Dec 29 2017
STATUS
approved