This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341993 #16 Mar 21 2021 18:20:52 %S A341993 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 A341993 56,15,16,17,18,19,38,76,21,42,84,168,23,46,92,184,368,25,27,29,58,30, %U A341993 60,31,62,32,64,128,256,33,66,34,68,35,36,37,74,148,296,39 %N A341993 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 A341993 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 A341993 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 A341993 Record values are 0, 1, 2, 4, 8, 9, 10, 20, 40, 80, 88, ... %H A341993 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a> %e A341993 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 A341993 Cf. A000079 (powers of 2), A331440 (similar principle, except lesser or equal sum of digits replaced by containing the digit S). %K A341993 nonn,base %O A341993 0,3 %A A341993 _Jamie Robert Creasey_, Feb 25 2021