A257796 - OEIS

%I #13 Jan 12 2019 02:27:31

%S 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,

%T 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,

%U 16,9,9,16,0,0,16,9,9,0

%N 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.

%C Six loops are possible. There are three loops of one.

%C 21.0% of the numbers end up as zero.

%C Some numbers end up as a happy number (=1); density is 4.2%.

%C Some numbers end up as 48; density is 4.8%.

%C More numbers end up in a loop of two (16 and 35); density is 25.4%.

%C Most numbers end up in a loop of five (9, 81, 63, 27, 45, 9); density is 44.6%.

%H Pieter Post, <a href="/A257796/b257796.txt">Table of n, a(n) for n = 1..999</a>

%e a(17)=48 because abs(1^2 - 7^2) = 48 => abs(4^2 - 8^2) = 48.

%e 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.

%Y Cf. A007770, A090425, A257588.

%K nonn,base

%O 1,2

%A _Pieter Post_, May 09 2015