A387487 a(n) is the length of the longest prefix of S matching the substring of S starting at n where S = 123456789101112... is the Champernowne word (A033307).

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

2,13

Comments

S is indexed from 1; that is, the first character of S has position 1.

Because S matches itself, a(1) = infinity.

This function (applied to any particular S) is called Z_n(S) in Gusfield and has implications for performing efficient string searching.

References

Dan Gusfield, Algorithms on Strings, Trees, and Sequences, Cambridge Univ. Press, 1997 (see Section 1.3).

Links

Sean A. Irvine, Table of n, a(n) for n = 2..1000

Prog

(Python)
from os.path import commonprefix
M = 3000  # produces 10889 terms
an, n, alst = 0, 2, []
C = "".join(str(i) for i in range(1, M+1))
while n+an < len(C):
    an, n = len(commonprefix([C[n-1:], C])), n+1
    alst.append(an)
alst = alst[:-1]
# Michael S. Branicky, Jan 30 2026

Crossrefs

Cf. A031297, A033307, A392989.

Sequence in context: A123671 A117145 A191261 * A355745 A348213 A355741

Adjacent sequences: A387484 A387485 A387486 * A387488 A387489 A387490

Keyword

nonn

Author

Sean A. Irvine, Jan 29 2026

Status

approved