|
| |
|
|
A175424
|
|
a(n) = number of steps of iterations of {(((D_k^D_(k-1))^D_(k-2))^...)^D_1, where D_k = k-th digit D of number r and k = the number digit of number r in decimal expansion of r (A055642)} needed to reach a single-digit number starting at r = n, or a(n) = -1 if a single-digit number is never reached.
|
|
7
|
|
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, -1, -1, 3, 3, 2, 1, 1, 1, 4, 3, -1, -1, 3, 3, 3, 1, 1, 2, 2, 3, 3, 3, 2, 2, 2, 1, 1, 2, 3, 2, 4, 3, 2, 3, 2, 1, 1, 3, 3, 2, 3, 3, 3, 3, 2, 1, 1, 4, 3, 3, 3, 3, 3, 2, 3, 1, 1, 3, 2, 3, 2, 3, 2, 2, 2, 1, 1, 3, 3, 3, 3, 2, 2, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,25
|
|
|
COMMENTS
|
Conjecture: max(a(n)) = 4.
|
|
|
LINKS
|
Table of n, a(n) for n=0..99.
|
|
|
EXAMPLE
|
For n = 33: a(33) = 4 because for the number 33 there are 4 steps of defined iteration: {3^3 = 27}, {7^2 = 49}, {9^4 = 6561}, {((1^6)^5)^6 = 1}.
|
|
|
CROSSREFS
|
Cf. A175419, A175420, A175421, A175422, A175423, A175425, A175426, A175427.
Sequence in context: A100640 A242779 A215065 * A144401 A034929 A099509
Adjacent sequences: A175421 A175422 A175423 * A175425 A175426 A175427
|
|
|
KEYWORD
|
sign,base
|
|
|
AUTHOR
|
Jaroslav Krizek, May 09 2010
|
|
|
STATUS
|
approved
|
| |
|
|
