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A257261
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One-based position of the rightmost one in the factorial base representation (A007623) of n, 0 if no one is present.
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5
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0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 4, 1, 2, 1, 4, 1, 3, 1, 2, 1, 3, 1, 4, 1, 2, 1, 4, 1, 4, 1, 2, 1, 4, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 5
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OFFSET
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0,3
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LINKS
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FORMULA
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Other identities:
For all n >= 1, a(n!) = n.
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EXAMPLE
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For n = 0, with factorial base representation (A007623) "0", there are no ones present at all, thus a(0) = 0.
For n = 1, with representation "1", the rightmost one occurs at digit-position 1 (when the least significant digit has index 1, etc.), thus a(1) = 1.
For n = 6, with representation "100", the rightmost one occurs at position 3, thus a(6) = 3.
For n = 11, with representation "121", the rightmost one occurs at digit-position 1 (when the least significant digit has index 1, etc.), thus a(11) = 1.
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MATHEMATICA
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a[n_] := Module[{k = n, m = 2, r, s = {}, p}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; If[MissingQ[(p = FirstPosition[s, 1])], 0, p[[1]]]]; Array[a, 100, 0] (* Amiram Eldar, Feb 07 2024 *)
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PROG
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(Scheme) (define (A257261 n) (let loop ((n n) (i 2)) (cond ((zero? n) 0) ((= 1 (modulo n i)) (- i 1)) (else (loop (floor->exact (/ n i)) (+ 1 i))))))
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CROSSREFS
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Cf. A000142 (positions of records, where each n first occurs as a value), A255411 (positions of zeros), A000012 (odd bisection).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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