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.

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

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

Pieter Post, Table of n, a(n) for n = 1..999

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

Cf. A007770, A090425, A257588.

Sequence in context: A302683 A302518 A070567 * A070688 A281719 A103167

Adjacent sequences: A257793 A257794 A257795 * A257797 A257798 A257799

Keyword

nonn,base

Author

Pieter Post, May 09 2015

Status

approved