A244417 Exponents of 6 in appearing in the 6-adic value of 1/n, n>=1 (A244416).

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

Author

Wolfdieter Lang, Jul 02 2014

Keywords

• nonn
• easy

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.

Examples

			See A244416.
		

References

• Kurt Mahler, p-adic numbers and their functions, second ed., Cambridge University Press, 1981.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..19683

Crossrefs

Cf. A122841, A244416, A007814 (g=2), A007949 (g=3), A244415 (g=4), A112765 (g=5), A051903, A065331.

Cf. also A322026, A322316.

Programs

Mathematica

a[n_] := Max[IntegerExponent[n, {2, 3}]]; Array[a, 100] (* Amiram Eldar, Aug 19 2024 *)

PARI

A244417(n) = max(valuation(n,2), valuation(n,3)); \\ Antti Karttunen, Dec 04 2018

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)