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A364377
The number of trailing 0's in the representation of n in Jacobsthal greedy base (A265747).
3
0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 3, 0, 0, 1, 0, 2, 0, 0, 1, 0, 4, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 3, 0, 0, 1, 0, 2, 0, 0, 1, 0, 4, 5, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 3, 0, 0, 1, 0, 2, 0, 0, 1, 0, 4, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 3, 0, 0, 1, 0, 2, 0, 0, 1, 0, 6, 0, 0
OFFSET
1,5
COMMENTS
The first position of k, for k = 0, 1, 2, ..., is A001045(k+2).
The asymptotic density of the occurrences of 2*k is 9/4^(k+2), and of 2*k+1 is 3/4^(k+2), both for k >= 0.
The asymptotic mean of this sequence is 11/12, and its asymptotic standard deviation is sqrt(283)/12.
LINKS
MATHEMATICA
a[n_] := IntegerExponent[A265747[n], 10]; Array[a, 100] (* using A265747[n] *)
PROG
(PARI) a(n) = valuation(A265747(n), 10); \\ using A265747(n)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jul 21 2023
STATUS
approved