A362468 -id:A362468 - 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)

A362556 Number of distinct n-digit suffixes generated by iteratively multiplying an integer by 8, where the initial integer is 1.

Original entry on oeis.org

5, 21, 101, 502, 2502, 12502, 62503, 312503, 1562503, 7812504, 39062504, 195312504, 976562505, 4882812505, 24414062505, 122070312506, 610351562506, 3051757812506, 15258789062507, 76293945312507, 381469726562507

Offset: 1

Gil Moses, Apr 24 2023

			For n = 1, we begin with 1, iteratively multiply by 8 and count the number of terms before the last 1 digit begins to repeat. We obtain 1, 8, 64, 512, 4096, ... . The next term is 32768, which repeats the last 1 digit 8. Thus, the number of distinct terms is a(1) = 5.

Paolo Xausa, Table of n, a(n) for n = 1..1000
Wikipedia, Multiplicative order
Index entries for linear recurrences with constant coefficients, signature (6,-5,1,-6,5).

Cf. A001018, A005054.
Cf. A014391, A014392.
Cf. A362468 (with 4 as the multiplier).

A362556[n_]:=5^(n-1)4+Ceiling[n/3];Array[A362556,30] (* after Charles R Greathouse IV *) (* or *) LinearRecurrence[{6,-5,1,-6,5},{5,21,101,502,2502},30] (* Paolo Xausa, Nov 18 2023 *)

a(n)=4*5^(n-1)+ceil(n/3) \\ Charles R Greathouse IV, Apr 28 2023

def a(n):
     s, x, M = set(), 1, 10**n
     while x not in s: s.add(x); x = (x<<3)%M
     return len(s)

a(13)-a(21) from Charles R Greathouse IV, Apr 28 2023

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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