A370557 -id:A370557 - cp's OEIS frontend

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

Gil Moses, Apr 24 2023

			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.

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).

Cf. A104745, A370557.

Cf. A362468 (with 4 as the multiplier).

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

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)

A221907 a(n) = 5^n + 5*n.

Original entry on oeis.org

1, 10, 35, 140, 645, 3150, 15655, 78160, 390665, 1953170, 9765675, 48828180, 244140685, 1220703190, 6103515695, 30517578200, 152587890705, 762939453210, 3814697265715, 19073486328220, 95367431640725, 476837158203230, 2384185791015735, 11920928955078240, 59604644775390745

Offset: 0

Vincenzo Librandi, Mar 02 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

Cf. A107585, A176916, A362555, A370557.

Magma
```
[5^n + 5*n: n in [0..30]];
```

I:=[1, 10, 35]; [n le 3 select I[n] else 7*Self(n-1)-11*Self(n-2)+5*Self(n-3): n in [1..30]];

Table[(5^n + 5 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 3 x - 24 x^2)/((1 - x)^2 (1 - 5 x)), {x, 0, 30}], x]
LinearRecurrence[{7,-11,5},{1,10,35},30] (* Harvey P. Dale, Jul 23 2013 *)

a(n)=5^n+5*n \\ Charles R Greathouse IV, Apr 18 2013

G.f.: (1+3*x-24*x^2)/((1-x)^2*(1-5*x)).
a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).
a(n) = A176916(n) - 1.
a(n) = 5*A362555(n) for n > 0. - Hugo Pfoertner, Mar 01 2024
E.g.f.: exp(x)*(exp(4*x) + 5*x). - Elmo R. Oliveira, Sep 10 2024

cp's OEIS Frontend

A362555 Number of distinct n-digit suffixes generated by iteratively multiplying an integer by 6, where the initial integer is 1.

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