A319317 -id:A319317 - cp's OEIS frontend

3, 9, 15, 27, 28, 29, 30, 31, 39, 45, 54, 55, 57, 63, 81, 82, 83, 84, 85, 87, 90, 91, 93, 94, 95, 99, 108, 109, 110, 111, 117, 118, 119, 123, 126, 127, 135, 162, 163, 165, 171, 174, 175, 183, 189, 190, 191, 207, 219, 243, 244, 245, 246, 247, 248, 249, 250, 251

Offset: 1

Jianing Song, Sep 17 2018

nonn

Numbers k such that the highest power of 12 dividing n! is determined by the highest power of 4 dividing n!.
Note that A054861 and A090616 are both asymptotic to a(n) = n/2 + O(log(n)), nevertheless, it seems that the number of k such that A090616(k) is bigger predominates. Conjecture: the ratio of k <= N such that A090616(k) > A054861(k) tends to 1 as N tends to infinity, while the ratio of k <= N such that A090616(k) < A054861(k) and A090616(k) = A054861(k) both tend to 0.
Number of k in range [0, N] such that A090616(k) =, < or > A054861(k):
..N....A090616(k) = A054861(k)...A090616(k) < A054861(k)...A090616(k) > A054861(k)
10^2...............38........................26........................37
10^3..............344.......................228.......................429
10^4.............2703......................2227......................5071
10^5............23003.....................19892.....................57106
10^6...........203478....................185152....................611371
10^7..........1762288...................1726062...................6511651

			The highest power of 3 dividing 9! is 3^4, while the highest power of 4 dividing 9! is 4^3, so 9 is a term, and the highest power of 12 dividing 9! is 12^3.
The highest power of 3 dividing 15! is 3^6, while the highest power of 4 dividing 15! is 4^5, so 15 is a term, and the highest power of 12 dividing 15! is 12^5.

Jianing Song, Table of n, a(n) for n = 1..2227 (all terms <= 10000)

Cf. A217445 (k such that A090616(k) = A054861(k)), A319317 (k such that A090616(k) > A054861(k)).

isA319316(n)=(n-vecsum(digits(n, 2)))\2<(n-vecsum(digits(n, 3)))\2

cp's OEIS Frontend

A319316 Numbers k such that A090616(k) < A054861(k).

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