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

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

Offset

1,1

Links

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).

Example

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.

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A001018, A005054.

Cf. A014391, A014392.

Cf. A362468 (with 4 as the multiplier).

Sequence in context: A338673 A199215 A204061 * A046633 A280623 A203154

Adjacent sequences: A362553 A362554 A362555 * A362557 A362558 A362559

Keyword

nonn,base,easy

Author

Gil Moses, Apr 24 2023

Extensions

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

Status

approved