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A244417
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Exponents of 6 in appearing in the 6-adic value of 1/n, n>=1 (A244416).
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8
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0, 1, 1, 2, 0, 1, 0, 3, 2, 1, 0, 2, 0, 1, 1, 4, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 3, 2, 0, 1, 0, 5, 1, 1, 0, 2, 0, 1, 1, 3, 0, 1, 0, 2, 2, 1, 0, 4, 0, 1, 1, 2, 0, 3, 0, 3, 1, 1, 0, 2, 0, 1, 2, 6, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 1, 0, 4, 4, 1, 0, 2, 0, 1, 1, 3, 0, 2, 0, 2, 1, 1, 0, 5, 0, 1, 2, 2
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OFFSET
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1,4
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COMMENTS
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For the definition of 'g-dic value of 1/n' see a comment on A244416. In the Mahler reference, p. 7, the present exponent of 6 is there called f = f(1/n) for g = 6.
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REFERENCES
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Kurt Mahler, p-adic numbers and their functions, second ed., Cambridge University Press, 1981.
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LINKS
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FORMULA
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a(n) = 0 if n is congruent 1 or 5 (mod 6). a(n) = max(A007814(n), A007949(n)) if n == 0 (mod 6). a(n) = A007814(n) if n == 2 or 4 (mod 6) and a(n) = A007949(n) if n == 3 (mod 6).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 13/10. (End)
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EXAMPLE
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MATHEMATICA
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a[n_] := Max[IntegerExponent[n, {2, 3}]]; Array[a, 100] (* Amiram Eldar, Aug 19 2024 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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