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.

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

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