1,1

Paolo Xausa, Table of n, a(n) for n = 1..1000

Wikipedia, Multiplicative Order

Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

a(n) = 5^(n-1) + n.

From Stefano Spezia, Apr 27 2023: (Start)

O.g.f.: (1 - 5*x + 4*x^2 - 4*x^3)/((1 - x)^2*(1 - 5*x)).

E.g.f.: (4 + exp(5*x) + 5*exp(x)*x)/4. (End)

For n = 2, we begin with 1, iteratively multiply by 6 and count the terms before the last 2 digits begin to repeat. We obtain 1, 6, 36, 216, 1296, 7776, 46656, ... . The next term is 279936, which repeats the last 2 digits 36. Thus, the number of distinct terms is a(2) = 7.

A362555[n_]:=5^(n-1)+n; Array[A362555, 30] (* Paolo Xausa, Nov 18 2023 *)

Cf. A104745, A370557.

Cf. A362468 (with 4 as the multiplier).

Sequence in context: A227845 A118926 A127084 * A252737 A217203 A052319

Adjacent sequences: A362552 A362553 A362554 * A362556 A362557 A362558

nonn,base,easy

Gil Moses, Apr 24 2023

approved