A340347 An aware-like sequence; empty the first pit/integer and sow its content to the right, one seed/unit per pit/integer. When this is done the new sequence and the starting one share the same succession of digits.

1, 109, 2, 8, 27, 3, 26, 31, 5, 4, 30, 53, 29, 52, 6, 28, 51, 61, 7, 50, 60, 9, 749, 59, 96, 48, 58, 95, 47, 57, 94, 10, 46, 56, 93, 103, 64, 68, 309, 35, 45, 829, 11, 92, 544, 81, 90, 18, 24

Offset

1,2

Comments

This sequence is the lexicographically earliest one of distinct integers > 0 and is conjectured to be a permutation of the integers > 0.

Links

Carole Dubois, Table of n, a(n) for n = 1..10347

Example

We start with a(1) = 1 and add 1 to a(2) to form b(1), the first term of the new sequence, thus b(1) = 109 + 1 = 110;
we go on from there with a(3) = 2 to form b(2) = 8 + 1 = 9 and b(3) = 27 + 1 = 28;
we go on from there with a(6) = 3 to form b(4) = 26 + 1 = 27 , b(5) = 31 + 1 = 32 and b(6) = 5 + 1 = 6;
we go on from there with a(10) = 4 to form b(7) = 30 + 1 = 31, b(8) = 53 + 1 = 54, b(9) = 29 + 1 = 30 and b(10) = 52 + 1 = 53; etc.
If we now compare the successive terms a(n) and b(n), we see that they share the same digit succession:
a(n) = 1, 109, 2, 8, 27, 3, 26, 31, 5, 4, 30, 53, 29, 52, ...
b(n) = 110, 9, 28, 27, 32, 6, 31, 54, 30, 53, ...

Crossrefs

Cf. A301743.

Sequence in context: A077728 A093724 A340348 * A247440 A130705 A253431

Adjacent sequences: A340344 A340345 A340346 * A340348 A340349 A340350

Keyword

nonn,look,base

Author

Eric Angelini, Jan 05 2021

Status

approved