OFFSET
0,3
COMMENTS
Inspired by A278586.
Lim_{n->inf} a(n)/(9/8)^n = 5.19544896392362185906460915572195169945039729234281...
FORMULA
a(n) = floor(a(n-1)*9/8) + 1.
EXAMPLE
12 -> 12-ceiling(12/9) = 10,
10 -> 10-ceiling(10/9) = 8,
8 -> 8-ceiling(8/9) = 7,
7 -> 7-ceiling(7/9) = 6,
...
1 -> 1-ceiling(1/9) = 0,
so reaching 0 from 12 requires 10 steps;
13 -> 13-ceiling(13/9) = 11,
11 -> 11-ceiling(11/9) = 9,
9 -> 9-ceiling(9/9) = 8,
8 -> 8-ceiling(8/9) = 7,
7 -> 7-ceiling(7/9) = 6,
...
1 -> 1-ceiling(1/9) = 0,
so reaching 0 from 13 (or more) requires 11 (or more) steps;
thus, 12 is the largest starting value from which 0 can be reached in 10 steps, so a(10) = 12.
PROG
(Magma) a:=[0]; aCurr:=0; for n in [1..56] do aCurr:=Floor(aCurr*9/8)+1; a[#a+1]:=aCurr; end for; a;
CROSSREFS
Cf. A278586.
See the following sequences for maximum starting value of X such that repeated replacement of X with X-ceiling(X/k) requires n steps to reach 0: A000225 (k=2), A006999 (k=3), A155167 (k=4, apparently; see Formula entry there), A279075 (k=5), A279076 (k=6), A279077 (k=7), A279078 (k=8), (this sequence) (k=9), A279080 (k=10). For each of these values of k, is the sequence the L-sieve transform of {k-1, 2k-1, 3k-1, ...}?
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Dec 06 2016
STATUS
approved