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.

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

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 + 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

Adjacent sequences: A297178 A297179 A297180 * A297182 A297183 A297184

Keyword

nonn

Author

N. J. A. Sloane, Dec 28 2017

Extensions

Terms a(21) and beyond from Lars Blomberg, Dec 29 2017

Status

approved