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
KEYWORD
easy,nonn
AUTHOR
Paul D. Hanna, Jul 29 2002
STATUS
approved