A297182 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 13.

1, 2, 3, 4, 5, 6, 7, 20, 33, 46, 59, 72, 85, 254, 423, 592, 761, 930, 1099, 3296, 5493, 7690, 9887, 12084, 14281, 42842, 71403, 99964, 128525, 157086, 185647, 556940, 928233, 1299526, 1670819, 2042112, 2413405, 7240214, 12067023, 16893832, 21720641, 26547450

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.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,13,-13).

Formula

Conjectures from Colin Barker, Dec 28 2017: (Start)

G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5 - 12*x^6) / ((1 - x)*(1 - 13*x^6)).

a(n) = a(n-1) + 13*a(n-6) - 13*a(n-7) for n>7.

(End)

The second conjecture by Colin Barker is true up to n=1000. - Lars Blomberg, Dec 29 2017

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 13, -13}, {1, 2, 3, 4, 5, 6, 7}, 50] (* Harvey P. Dale, May 31 2023 *)

Crossrefs

Sequence in context: A037342 A200333 A024644 * A010354 A070759 A282138

Adjacent sequences: A297179 A297180 A297181 * A297183 A297184 A297185

Keyword

nonn

Author

N. J. A. Sloane, Dec 28 2017

Extensions

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

Status

approved