A187187 Parse the infinite string 0123456780123456780123456780... into distinct phrases 0, 1, 2, 3, 4, 5, 6, 7, 8, 01, 23, 45, 67, 80, 12, 34, 56, 78, 012, ...; a(n) = length of n-th phrase.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 13, 12, 12, 12, 13, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14

Offset: 1

Author

N. J. A. Sloane, Mar 06 2011

Keywords

• nonn
• easy

Comments

See A187180 for details.

Links

• Ray Chandler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Crossrefs

See A187180-A187188 for alphabets of size 2 through 10.

Formula

After the initial block of nine 1's, the sequence is quasi-periodic with period 81, increasing by 9 after each block.