A187186 Parse the infinite string 0123456701234567012345670... into distinct phrases 0, 1, 2, 3, 4, 5, 6, 7, 01, 23, 45, 67, 012, 34, ...; a(n) = length of n-th phrase.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5, 4, 4, 5, 4, 4, 5, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 10, 10, 10, 10, 11, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 13, 12, 12, 13, 12, 12, 13, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15

Offset

1,9

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, 1, -1).

Formula

After the initial block of eight 1's, the sequence is quasi-periodic with period 64, increasing by 8 after each block.

a(n) ~ n/8. - Charles R Greathouse IV, May 30 2026

Prog

(PARI) a(n)=if(n>7, (n+[8, -1, 6, -3, 4, -5, 2, -7, 0, 7, 6, 5, 4, 11, 2, 1, 0, -1, 6, 5, 4, 3, 2, 1, 0, 7, 6, 13, 4, 3, 10, 1, 0, 7, -2, -3, 4, 3, 2, 1, 0, 7, 6, 5, 4, 11, 2, 1, 0, -1, 6, 5, 4, 3, 2, 1, 0, 7, 14, 5, 12, 3, 10, 1][n%64+1])/8, 1) \\ Charles R Greathouse IV, May 30 2026

Crossrefs

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

Sequence in context: A067131 A094915 A217619 * A259651 A253719 A081147

Adjacent sequences: A187183 A187184 A187185 * A187187 A187188 A187189

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 06 2011

Status

approved