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
Examples
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.
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).
Programs
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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 *)
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PARI
a(n)=4*5^(n-1)+ceil(n/3) \\ Charles R Greathouse IV, Apr 28 2023
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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)
Extensions
a(13)-a(21) from Charles R Greathouse IV, Apr 28 2023