A073360 Nested floor product of n and fractions (k+1)/k for all k>0 (mod 3), divided by 3.

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

Offset

1,2

Links

Paul D. Hanna, Table of n, a(n) for n = 1..300

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

Adjacent sequences: A073357 A073358 A073359 * A073361 A073362 A073363

Keyword

easy,nonn,changed

Author

Paul D. Hanna, Jul 29 2002

Status

approved