A351378 For all a(2n) the cumulative sum of the even digits used so far in the sequence [including a(2n)] is twice the cumulative sum of the odd digits used so far in the sequence [including a(2n)]. This is the lexicographically earliest sequence of distinct positive numbers with this property.
1, 2, 3, 6, 4, 11, 5, 28, 7, 68, 8, 13, 9, 288, 10, 14, 12, 21, 15, 48, 16, 23, 17, 88, 18, 30, 19, 488, 20, 34, 22, 32, 24, 45, 25, 26, 27, 66, 29, 268, 31, 44, 33, 84, 35, 286, 36, 63, 37, 668, 38, 43, 39, 888, 40, 56, 41, 58, 42, 54, 46, 47, 49, 86, 50, 64, 51, 168, 52, 62, 53, 448, 55, 686, 57, 2688, 59
Offset: 1
Examples
This sequence : 1, 2, 3, 6, 4, 11, 5, 28, 7, 68, 8, 13, 9, 288, 10, 14, 12 ...
Even dig. sums: 0, 2, 2, 8, 12, 12, 12, 22, 22, 36, 44, 44, 44, 62, 62, 66, 68 ...
Odd dig. sums : 1, 1, 4, 4, 4, 6, 11, 11, 18, 18, 18, 22, 31, 31, 32, 33, 34 ...
x x x x x x x x ...
We see that 2 is twice 1, 8 is twice 4, 12 is twice 6, 22 is twice 11, 36 is twice 18, etc.
Links
- Carole Dubois, Table of n, a(n) for n = 1..10000
- Eric Angelini, Une merveille avec a(2n), Feb 8, 2022, personal blog (in French).
- Index entries for sequences that are permutations of the natural numbers
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