|
Search: id:A072137
|
|
|
| A072137 |
|
Length of the preperiodic part of the 'Reverse and Subtract' trajectory of n. |
|
+0
18
|
|
| 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 1, 2, 6, 4
(list; graph; listen)
|
|
|
OFFSET
|
0,11
|
|
|
COMMENT
|
'Reverse and Subtract' (cf. A070837, A070838) is defined by x -> |x - reverse(x)|, where reverse(x) is the digit reversal of x.
For every n the trajectory eventually becomes periodic, since 'Reverse and Subtract' does not increase the number of digits and so the set of available terms is finite. For small n the period length is 1, the periodic part consists of 0's, the last term of the preperiodic part is a palindrome.
The first n with period length 2 and a nontrivial periodic part is 1012 (cf. A072140).
This sequence is a weak analogue of A033665, which uses 'Reverse and Add'.
|
|
EXAMPLE
|
a(15) = 4 since 15 -> |15- 51| = 36 -> |36 - 63| = 27 -> |27 - 72| = 45 -> |45 - 54| = 9.
|
|
CROSSREFS
|
Cf. A033665, A070837, A070838, A072138, A072139, A072140, A072141, A072146, A072147.
Sequence in context: A126093 A065279 A069627 this_sequence A061569 A094965 A025277
Adjacent sequences: A072134 A072135 A072136 this_sequence A072138 A072139 A072140
|
|
KEYWORD
|
base,easy,nonn,nice
|
|
AUTHOR
|
Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 24 2002
|
|
|
Search completed in 0.002 seconds
|
