A362555 Number of distinct n-digit suffixes generated by iteratively multiplying an integer by 6, where the initial integer is 1.
2, 7, 28, 129, 630, 3131, 15632, 78133, 390634, 1953135, 9765636, 48828137, 244140638, 1220703139, 6103515640, 30517578141, 152587890642, 762939453143, 3814697265644, 19073486328145, 95367431640646, 476837158203147, 2384185791015648, 11920928955078149, 59604644775390650
Offset: 1
Examples
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.
Links
- 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).
Programs
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Mathematica
A362555[n_]:=5^(n-1)+n;Array[A362555,30] (* Paolo Xausa, Nov 18 2023 *)
Formula
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)