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.

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, 56, 15, 16, 17, 18, 19, 38, 76, 21, 42, 84, 168, 23, 46, 92, 184, 368, 25, 27, 29, 58, 30, 60, 31, 62, 32, 64, 128, 256, 33, 66, 34, 68, 35, 36, 37, 74, 148, 296, 39

Offset: 0

Author

Jamie Robert Creasey, Feb 25 2021

Keywords

• nonn
• base

Comments

This sequence is a permutation of the nonnegative integers; the inverse permutation begins 0, 1, 2, 5, 3, 7, 6, 8, 4, 9, 10, ...

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).

Record values are 0, 1, 2, 4, 8, 9, 10, 20, 40, 80, 88, ...

Examples

			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.
		

Links

• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A000079 (powers of 2), A331440 (similar principle, except lesser or equal sum of digits replaced by containing the digit S).