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A073360 Nested floor product of n and fractions (k+1)/k for all k>0 (mod 3), divided by 3. 5
1, 4, 9, 20, 29, 44, 69, 104, 121, 180, 241, 284, 349, 420, 521, 664, 701, 860, 1009, 1184, 1301, 1540, 1789, 1964, 2181, 2380, 2701, 3124, 3301, 3704, 4029, 4444, 4809, 5144, 5789, 6340, 6729, 7244, 7981, 8420, 9101 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n)=(1/3)[...[[[[n(2/1)](3/2)](5/4)](6/5)]...(k+1)/k]..., k>0 (mod 3), where [x] = floor of x; this infinite nested floor product will eventually level-off at a(n).
EXAMPLE
a(2) = 4 since (1/3)[[[[[[2(2/1)](3/2)](5/4)](6/5)](8/7)](9/8)](11/10)](12/11)]
= (1/3)[[[[[4(3/2)](5/4)](6/5)](8/7)](9/8)](11/10)](12/11)]
= (1/3)[[[[6(5/4)](6/5)](8/7)](9/8)](11/10)](12/11)]
= (1/3)[[[[7(6/5)](8/7)](9/8)](11/10)](12/11)]
= (1/3)[[[[8(8/7)](9/8)](11/10)](12/11)]
= (1/3)[[[[9(9/8)](11/10)](12/11)]
= (1/3)[[[[10(11/10)](12/11)]
= 4.
Note that the denominators consist of positive integers not == 0 mod 3.
CROSSREFS
Cf. A073359.
Sequence in context: A030734 A368587 A212101 * A297190 A075385 A048150
KEYWORD
easy,nonn
AUTHOR
Paul D. Hanna, Jul 29 2002
STATUS
approved

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Last modified June 18 14:09 EDT 2024. Contains 373481 sequences. (Running on oeis4.)