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A007844
Least positive integer k for which 3^n divides k!.
6
1, 3, 6, 9, 9, 12, 15, 18, 18, 21, 24, 27, 27, 27, 30, 33, 36, 36, 39, 42, 45, 45, 48, 51, 54, 54, 54, 57, 60, 63, 63, 66, 69, 72, 72, 75, 78, 81, 81, 81, 81, 84, 87, 90, 90, 93, 96, 99, 99, 102, 105, 108, 108, 108, 111, 114, 117, 117, 120, 123, 126, 126, 129, 132, 135, 135, 135
OFFSET
0,2
COMMENTS
It appears than for n>0, a(n) is divisible by 3, and that the resulting sequence a(n)/3 is A120503 (checked up to n=1000). - Michel Marcus, Aug 19 2013. [This is true: see A007843 for the idea of the proof. - M. F. Hasler, Dec 27 2019]
Also least positive integer k for which 6^n divides k!. - Michel Marcus, Aug 20 2013
REFERENCES
H. Ibstedt, Smarandache Primitive Numbers, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 216-229.
FORMULA
a(n) = 3*A120503(n) for n > 0, cf. A007843. - M. F. Hasler, Dec 27 2019
MATHEMATICA
Array[Block[{k = 1}, While[Mod[k!, 3^#] != 0, k++]; k] &, 67, 0] (* Michael De Vlieger, Dec 29 2019 *)
PROG
(PARI) a(n) = {k = 1; while (valuation(k!, 3) < n, k++); k; } \\ Michel Marcus, Aug 19 2013
(PARI) apply( A007844(n)={my(s=sumdigits(n*=2, 3)\2); n-=n%3; while(s>0, s-=valuation(n+=3, 3)); n+!n}, [0..99]) \\ M. F. Hasler, Dec 27 2019
CROSSREFS
Cf. A007843 (analog for 2), A007845 (analog for 5).
Cf. A120503 (Meta-Fibonacci, k = 3).
Sequence in context: A011383 A329513 A329213 * A224523 A159785 A057338
KEYWORD
nonn
AUTHOR
Bruce Dearden and Jerry Metzger, R. Muller
STATUS
approved