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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.
2
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
1,2
COMMENTS
The sequence is a permutation of the positive integers.
EXAMPLE
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.
CROSSREFS
Sequence in context: A073318 A254047 A049449 * A104663 A358299 A246429
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Carole Dubois, Feb 09 2022
STATUS
approved