A118759 -id:A118759 - cp's OEIS frontend

A118761 Fixed points of permutations A118757, A118758, A118759 and A118760.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 119, 138, 157, 176, 195, 310, 339, 358, 377, 396, 559, 578, 597, 779, 798, 999, 3130

Offset: 1

Reinhard Zumkeller, May 01 2006

nonn

A118757(a(n)) = A118758(a(n)) = A118759(a(n)) = A118760(a(n)) = a(n);

a(n) = A024657(n-1) = A102491(n) for n<=50.

Cf. A118767.

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.

Original entry on oeis.org

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

Reinhard Zumkeller, May 01 2006

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

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

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).

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.

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

A118760 A118758(A118758(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 118, 108, 127, 126

Offset: 0

Reinhard Zumkeller, May 01 2006

nonn

Inverse integer permutation of A118759; a(n)=A118759(n) for n<100; A118757(a(n))=a(A118757(n))=A118758(n).

Tanya Khovanova, Non Recursions
Index entries for sequences that are permutations of the natural numbers

Cf. A118759.

cp's OEIS Frontend

A118761 Fixed points of permutations A118757, A118758, A118759 and A118760.

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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.

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A118760 A118758(A118758(n)).

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