A245628 Sequence has property that when divided into chunks by cutting it before each digit '1', each chunk contains exactly one 1, two 2's, three 3's, ..., and nine 9's. See Comments for more detailed definition.

1, 2, 23, 3, 34, 4, 44, 5, 55, 556, 6, 66, 667, 7, 77, 777, 8, 88, 888, 889, 9, 99, 999, 991, 22, 33, 344, 445, 555, 56, 666, 6677, 7777, 78, 8888, 8889, 9999, 99991, 223, 334, 444, 5555, 566, 6666, 77777, 778, 88888, 8899, 99999, 9912, 233, 3444, 45, 55556

Offset

1,2

Comments

Created in an attempt to capture the intention of Amarnath Murthy's A110354. (That entry is beyond repair.)

Here is Eric Angelini's description: (Start)

Cut the sequence into successive chunks of digits such that all chunks start with the digit '1'. Every chunk must now contain exactly one digit 1, two digits 2, three digits 3, ..., nine digits 9. The sequence is always extended with the smallest unused integer not leading to a contradiction such that any chunk 'c' shows first the required quantity of 1's, then the required quantity of 2's, then the 3's, ..., 9's.

The first chunk starts with a(1)=1 and ends with the second digit of "991". This chunk contains exactly one 1, two 2's, three 3's, etc. Note that a(3) cannot be equal to "3" because the required quantity of 2's is not yet reached in the chunk; neither can we have a(3)="12" as the chunk would contain two 1's; thus a(3)="23". The second chunk starts with the last digit of "991" and ends with the fourth digit of "99991". The third chunk starts with the last digit of "99991" and continues with "223" as this is the smallest available integer not leading to a contradiction, etc. (End) (adapted by Jens Kruse Andersen to match corrected sequence)

The concatenation of all terms is "122333444455555666666777777788888888999999999" repeated forever. This infinite string is split into integers by always picking the shortest unused substring. - Jens Kruse Andersen, Jul 29 2014

References

Eric Angelini, Email to N. J. A. Sloane, Jul 27 2014

Links

Table of n, a(n) for n=1..54.

Crossrefs

Cf. A110354.

Sequence in context: A076653 A114008 A110354 * A162711 A120713 A309154

Adjacent sequences: A245625 A245626 A245627 * A245629 A245630 A245631

Keyword

nonn,base

Author

N. J. A. Sloane, Jul 27 2014, based on correspondence with Eric Angelini

Extensions

Sequence corrected by Jens Kruse Andersen, Jul 29 2014

Status

approved