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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
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OFFSET
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1,1
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COMMENTS
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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):
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
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LINKS
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EXAMPLE
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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.
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PROG
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(PARI) isA319316(n)=(n-vecsum(digits(n, 2)))\2<(n-vecsum(digits(n, 3)))\2
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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