

A351406


For all a(2n) the cumulative sum of the odd digits used so far in the sequence [including a(2n)] is twice the cumulative sum of the even digits used so far in the sequence [including a(2n)]. This is the lexicographically earliest sequence of distinct numbers >= 0 with this property.


2



0, 123, 1, 23, 2, 13, 3, 12, 4, 17, 5, 34, 6, 39, 7, 14, 8, 79, 9, 36, 10, 32, 11, 112, 15, 114, 16, 119, 18, 159, 19, 116, 20, 31, 21, 27, 22, 35, 24, 57, 25, 47, 26, 97, 28, 1199, 29, 43, 30, 45, 33, 141, 37, 158, 38, 139, 40, 53, 41, 70, 42, 75, 44, 709, 46
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OFFSET

1,2


COMMENTS

The sequence is a permutation of the nonnegative integers.


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).
Carole Dubois, Comparative graphs for A351406 and A351378
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

This sequence : 0, 123, 1, 23, 2, 13, 3, 12, 4, 17, 5, 34, 6, 39, 7, 14, 8, ...
Even dig. sums: 0, 2, 2, 4, 6, 6, 6, 8, 12, 12, 12, 16, 22, 22, 22, 26, 34, ...
Odd dig. sums : 0, 4, 5, 8, 8, 12, 15, 16, 16, 24, 29, 32, 32, 44, 51, 52, 52, ...
x x x x x x x x ...
We see that 4 is twice 2, 8 is twice 4, 12 is twice 6, 16 is twice 8, 24 is twice 12, etc.


CROSSREFS

Cf. A001477, A036301, A351378.
Sequence in context: A015079 A015042 A062233 * A123171 A125097 A302211
Adjacent sequences: A351403 A351404 A351405 * A351407 A351408 A351409


KEYWORD

nonn,base,look


AUTHOR

Eric Angelini and Carole Dubois, Feb 10 2022


STATUS

approved



