|
|
A257796
|
|
Smallest value of the loop in which n ends, when iterating the map (A257588) which sends a number to absolute value of first digit squared minus second digit squared plus third digit squared etc.
|
|
6
|
|
|
1, 16, 9, 16, 9, 9, 0, 16, 9, 1, 0, 9, 16, 9, 9, 16, 48, 9, 16, 16, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 16, 9, 0, 0, 16, 9, 16, 0, 9, 16, 9, 9, 0, 0, 9, 16, 0, 48, 0, 9, 9, 9, 16, 9, 0, 0, 9, 9, 0, 9, 16, 9, 9, 16, 0, 0, 16, 9, 9, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Six loops are possible. There are three loops of one.
21.0% of the numbers end up as zero.
Some numbers end up as a happy number (=1); density is 4.2%.
Some numbers end up as 48; density is 4.8%.
More numbers end up in a loop of two (16 and 35); density is 25.4%.
Most numbers end up in a loop of five (9, 81, 63, 27, 45, 9); density is 44.6%.
|
|
LINKS
|
|
|
EXAMPLE
|
a(17)=48 because abs(1^2 - 7^2) = 48 => abs(4^2 - 8^2) = 48.
a(34)=0 because abs(3^2 - 4^2) = 7 => 7^2 = 49 => abs(4^2 - 9^2) = 65 => abs(6^2 - 5^2) = 11 => abs(1^2 - 1^2) = 0.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|