A118758 -id:A118758 - 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.

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.

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

A118764 Inverse of A118763.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 21, 22, 23, 24, 25, 26, 27, 28, 20, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 30, 41, 42, 43, 44, 45, 46, 47, 48, 40, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 50, 61, 62, 63, 64, 65, 66, 67, 68, 60, 69, 71, 72, 73

Offset: 0

Reinhard Zumkeller, May 01 2006

nonn

Permutation of the natural numbers with fixed points A118767: a(A118767(n))=A118767(n);

A118766(n) = a(a(n)).

Robert G. Wilson v, Table of n, a(n) for n = 0..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A118758.

(* first do Mmca in A118763, then *) Flatten@ Table[Position[s, n], {n, 0, 100}] - 1 (* Robert G. Wilson v, Sep 22 2016 *)

A118759 A118757(A118757(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, 189

Offset: 0

Reinhard Zumkeller, May 01 2006

nonn

Inverse integer permutation of A118760; a(n)=A118760(n)=n for n<100, but a(100)=189 and A118760(100)=118; A118758(a(n))=a(A118758(n))=A118757(n).

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

Cf. A118760.

More terms from Charles R Greathouse IV, Sep 18 2015

A261725 Lexicographically earliest sequence of distinct terms such that the absolute difference of two successive terms is a power of 10, and can be computed without carry.

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

Offset: 0

Paul Tek, Aug 30 2015

In base 10, two successive terms have the same representation, except for one position, where the digits differ from exactly one unit. This difference can occur on a leading zero.
Conjectured to be a permutation of the nonnegative integers. See A261729 for putative inverse.
a(n) = A003100(n) for n < 101, but a(101) = 180, A003100(101) = 191.
a(n) = A118757(n) for n < 201, but a(201) = 281, A118757(201) = 290.
a(n) = A118758(n) for n < 100, but a(100) = 190, A118758(100) = 109.
a(n) = A174025(n) for n < 100, but a(100) = 190, A174025(100) = 199.
a(n) = A261729(n) for n < 100, but a(100) = 190, A261729(100) = 109.

Paul Tek, Table of n, a(n) for n = 0..10000
Paul Tek, PERL program for this sequence

Cf. A003100, A118757, A118763, A163252, A261729 (putative inverse).

Perl
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See Links section.
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A261729 Putative inverse of conjectured permutation in A261725.

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

Offset: 0

Paul Tek, Aug 30 2015

a(n) = A003100(n) for n < 100, but a(100) = 109, A003100(100) = 190.
a(n) = A118757(n) for n < 100, but a(100) = 109, A118757(100) = 190.
a(n) = A118758(n) for n < 201, but a(201) = 209, A118758(201) = 211.
a(n) = A174025(n) for n < 100, but a(100) = 109, A174025(100) = 199.
a(n) = A261725(n) for n < 100, but a(100) = 109, A261725(100) = 190.

Paul Tek, Table of n, a(n) for n = 0..10000

Cf. A261725.

cp's OEIS Frontend

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

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A118760 A118758(A118758(n)).

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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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A118764 Inverse of A118763.

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Mathematica

A118759 A118757(A118757(n)).

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A261725 Lexicographically earliest sequence of distinct terms such that the absolute difference of two successive terms is a power of 10, and can be computed without carry.

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Perl

A261729 Putative inverse of conjectured permutation in A261725.

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