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A244417
Exponents of 6 in appearing in the 6-adic value of 1/n, n>=1 (A244416).
9
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
OFFSET
1,4
COMMENTS
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.
REFERENCES
Kurt Mahler, p-adic numbers and their functions, second ed., Cambridge University Press, 1981.
LINKS
FORMULA
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).
a(n) = max(A007814(n), A007949(n)), in all cases. - Antti Karttunen, Dec 04 2018
From Amiram Eldar, Aug 19 2024: (Start)
a(n) = A051903(A065331(n)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 13/10. (End)
EXAMPLE
See A244416.
MATHEMATICA
a[n_] := Max[IntegerExponent[n, {2, 3}]]; Array[a, 100] (* Amiram Eldar, Aug 19 2024 *)
PROG
(PARI) A244417(n) = max(valuation(n, 2), valuation(n, 3)); \\ Antti Karttunen, Dec 04 2018
CROSSREFS
Cf. A122841, A244416, A007814 (g=2), A007949 (g=3), A244415 (g=4), A112765 (g=5), A051903, A065331.
Cf. also A322026, A322316.
Sequence in context: A187496 A352552 A193056 * A324811 A086780 A158612
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jul 02 2014
STATUS
approved