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

Author

Pieter Post, May 09 2015

Keywords

• nonn
• base

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%.

Examples

			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.
		

Links

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

Crossrefs

Cf. A007770, A090425, A257588.