A118757 Permutation of the natural numbers such that the Levenshtein distance between decimal representations of successive terms is 1, and a(n+1) is the largest such m < a(n) if it exists, or else the smallest such m > a(n); a(0) = 0.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 79, 78, 77

Offset: 0

Author

Reinhard Zumkeller, May 01 2006

Keywords

• nonn
• base
• look

Comments

a(n) = A003100(n) for n <= 100, a(100) = A003100(100) = 190, but a(101) = 180, A003100(101) = 191.

A118763 is the lexicographically smallest permutation with LevenshteinDistance[Base10](a(n),a(n+1)) = 1. - M. F. Hasler, Sep 12 2018

Links

• R. Zumkeller, Table of n, a(n) for n = 0..30000
• Michael Gilleland, Levenshtein Distance, 2006. [Broken link fixed by _M. F. Hasler_, Sep 12 2018, cf A118763]
• R. Zumkeller, Values of A118757 for n<=1200
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A118763.

Iterated twice: A118759(n) := a(a(n)).

Fixed points: A118761 = { n | n = a(n) }.

Inverse: A118758.

First difference: A118762(n) := a(n+1) - a(n).

Formula

a(n+1) = if U(n) is empty then Min(V(n)) else Max(U(n)), where the sets U and V are defined as: U(m) = {x < a(m) : LD10(a(m),x) = 1 and a(k) <> x for 0 <= k < m}, V(m) = {x > a(m) | LD10(a(m),x) = 1 and a(k) <> x for 0 <= k < m} with LD10 = Levenshtein distance in decimal representations of natural numbers.

a(n) = A118758(n) (self-inverse) for n < 100.

Extensions

Correct definition and other edits by M. F. Hasler, Sep 12 2018