%I
%S 0,1,2,4,8,3,6,5,7,9,10,20,40,80,11,22,44,88,12,24,48,96,13,26,14,28,
%T 56,15,16,17,18,19,38,76,21,42,84,168,23,46,92,184,368,25,27,29,58,30,
%U 60,31,62,32,64,128,256,33,66,34,68,35,36,37,74,148,296,39
%N a(0)=0. For n > 0, a(n+1) = 2*a(n) if the sum of digits of 2*a(n) exceeds that of a(n); otherwise, a(n+1) is the smallest unused nonnegative integer.
%C This sequence is a permutation of the nonnegative integers; the inverse permutation begins 0, 1, 2, 5, 3, 7, 6, 8, 4, 9, 10, ...
%C There exist areas that feature numbers in runs of three or more in arithmetic progression, such as (5, 7, 9) and (15, 16, 17, 18, 19).
%C Record values are 0, 1, 2, 4, 8, 9, 10, 20, 40, 80, 88, ...
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%e We start the sequence with 0. Doubling this integer results in 0, but as the sum of digits of 0 is equal to that of 0, we choose the smallest nonnegative integer not yet used, which is 1. We can double 1 three times before the sum of digits of 2*a(n) (i.e., 16) does not exceed that of a(n) (8). Thus the next term after 8 is the next unused nonnegative integer, 3, after which we resume doubling.
%Y Cf. A000079 (powers of 2), A331440 (similar principle, except lesser or equal sum of digits replaced by containing the digit S).
%K nonn,base
%O 0,3
%A _Jamie Robert Creasey_, Feb 25 2021
