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

1,2

Comments

The sequence is a permutation of the positive 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).

Index entries for sequences that are permutations of the natural numbers

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

Cf. A036301, A351406.

Sequence in context: A073318 A254047 A049449 * A104663 A358299 A246429

Adjacent sequences: A351375 A351376 A351377 * A351379 A351380 A351381

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Feb 09 2022

Status

approved