A261160 List run lengths of digits different from '0'. Lexicographically first such sequence of nonnegative numbers with no repeated terms.

2, 1, 0, 100, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 10, 62, 20, 63, 110, 64, 65, 30, 66, 67, 120, 68, 69, 71, 40, 72, 73, 74, 130, 75, 76, 77, 78, 50

Offset

1,1

Comments

See A261161-A261163 for comments and examples.

Links

Table of n, a(n) for n=1..81.

E. Angelini, To reach the next "1", SeqFan list, August 10, 2015.

Example

The sequence cannot start with a(1) = 0 (which would require to start with 0 digits different from '0', contradiction) nor with a(1) = 1 (which would require to have a(2) = 0 and thus a chunk of 0 digits different from '0' after a(2), i.e., have a(3) start with another digit '0', which is impossible).
Thus, a(1) = 2.
Hence, a(2) starts with a nonzero digit, which must be followed by a digit '0'. It is indeed possible to choose a(2) = 1 and a(3) = 0.
Then must follow one nonzero digit and two consecutive digits '0'. Since the term 0 cannot appear for a second time, the "least" way to achieve this is to use a(4) = 100.
Then must follow 100 nonzero digits, viz the zeroless numbers from a(5) = 3 to a(57) = 61, followed by a(58) = 10.
From there on, to produce the zeroless chunks of length 3, 4, 5, ..., the lexico-first choice is 62, 20; 63, 110; 64, 65, 30; 66, 67, 120; and so on.

Crossrefs

Cf. A261161 - A261169 for the variants which use digit '1', ..., '9' as delimiter.

Sequence in context: A077019 A139037 A108511 * A270668 A196272 A086073

Adjacent sequences: A261157 A261158 A261159 * A261161 A261162 A261163

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Aug 10 2015

Status

approved