A118763 -id:A118763 - cp's OEIS frontend

A118764 Inverse of A118763.

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 *)

A118765 A118763(A118763(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17, 27, 28, 20, 21, 22, 23, 24, 25, 26, 29, 38, 39, 30, 31, 32, 33, 34, 35, 36, 37, 47, 48, 40, 41, 42, 43, 44, 45, 46, 49, 58, 59, 50, 51, 52, 53, 54, 55, 56, 57, 67, 68, 60, 61, 62, 63, 64, 65, 66, 69, 78, 79, 70

Offset: 0

Reinhard Zumkeller, May 01 2006

nonn

Inverse integer permutation of A118766;

A118764(a(n)) = a(A118764(n)) = A118763(n).

Index entries for sequences that are permutations of the natural numbers

Cf. A118766.

A118767 Fixed points of permutations A118763, A118764, A118765 and A118766.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 29, 49, 69, 89

Offset: 1

Reinhard Zumkeller, May 01 2006

A118763(a(n)) = A118764(a(n)) = A118765(a(n)) = A118766(a(n)) = a(n).

No more terms less than 10^4. Looking at the pattern mod 9, I conjecture that there will be more terms past 10^8. - Joshua Zucker, May 14 2006

Cf. A118761.

A118768 First differences of A118763.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, -9, 1, 1, 1, 1, 1, 1, 1, 1, 10, -8, 1, 1, 1, 1, 1, 1, 1, 2, 10, -9, 1, 1, 1, 1, 1, 1, 1, 1, 10, -8, 1, 1, 1, 1, 1, 1, 1, 2, 10, -9, 1, 1, 1, 1, 1, 1, 1, 1, 10, -8, 1, 1, 1, 1, 1, 1, 1, 2, 10, -9, 1, 1, 1, 1, 1, 1, 1, 1, 10, -8, 1, 1, 1, 1, 1, 1, 1, 2, 10, -9, 1, 1, 1, 1, 1, 1, 1, 1, 100, -90, -8, 1, 1, 1, 1, 1, 1, 1, 2, 10, -9, 1, 1, 1

Offset: 1

Reinhard Zumkeller, May 01 2006

sign

Cf. A118762.

a(n) = A118763(n+1) - A118763(n).

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

A118766 A118764(A118764(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11, 22, 23, 24, 25, 26, 27, 28, 20, 21, 29, 32, 33, 34, 35, 36, 37, 38, 39, 30, 31, 42, 43, 44, 45, 46, 47, 48, 40, 41, 49, 52, 53, 54, 55, 56, 57, 58, 59, 50, 51, 62, 63, 64, 65, 66, 67, 68, 60, 61, 69, 72, 73, 74

Offset: 0

Reinhard Zumkeller, May 01 2006

nonn

Inverse integer permutation of A118765;

A118763(a(n)) = a(A118763(n)) = A118764(n).

Index entries for sequences that are permutations of the natural numbers

Cf. A118765.

A367812 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 2.

Original entry on oeis.org

0, 11, 2, 10, 3, 12, 4, 13, 5, 14, 6, 15, 7, 16, 8, 17, 9, 18, 20, 1, 22, 19, 21, 30, 23, 31, 24, 32, 25, 33, 26, 34, 27, 35, 28, 36, 29, 37, 40, 38, 41, 39, 42, 50, 43, 51, 44, 52, 45, 53, 46, 54, 47, 55, 48, 56, 49, 57, 60, 58, 61, 59, 62, 70, 63, 71, 64, 72, 65, 73, 66, 74, 67, 75, 68, 76, 69, 77, 80, 78

Offset: 1

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

			a(1) =  0 and a(2) = 11 are separated by an Ld of 2
a(2) = 11 and a(3) =  2 are separated by an Ld of 2
a(3) =  2 and a(4) = 10 are separated by an Ld of 2
a(4) = 10 and a(5) =  3 are separated by an Ld of 2, etc.

Éric Angelini, More Levenshtein distances, Personal blog, December 2023.

Cf. A118763, A367813, A367814, A367815.

a[1]=0;a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n-1],k]||EditDistance[ToString@a[n-1],ToString@k]!=2,k++];k);Array[a,80]

from itertools import islice
from Levenshtein import distance as Ld
def agen(): # generator of terms
    an, aset, mink = 0, {0}, 1
    while True:
        yield an
        s, k = str(an), mink
        while k in aset or Ld(s, str(k)) != 2: k += 1
        an = k
        aset.add(k)
        while mink in aset: mink += 1
print(list(islice(agen(), 80))) # Michael S. Branicky, Dec 01 2023

A367813 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 3.

Original entry on oeis.org

0, 111, 2, 100, 3, 101, 4, 102, 5, 103, 6, 104, 7, 105, 8, 106, 9, 107, 21, 108, 22, 109, 23, 110, 24, 112, 20, 113, 25, 114, 26, 115, 27, 116, 28, 117, 29, 118, 30, 119, 32, 140, 31, 120, 33, 121, 34, 122, 35, 123, 36, 124, 37, 125, 38, 126, 39, 127, 40, 128, 41, 129, 43, 150, 42, 130, 44, 131, 45, 132, 46, 133

Offset: 1

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

			a(1) =   0 and a(2) = 111 are separated by a Ld of 3
a(2) = 111 and a(3) =   2 are separated by a Ld of 3
a(3) =   2 and a(4) = 100 are separated by a Ld of 3
a(4) = 100 and a(5) =   3 are separated by a Ld of 3, etc.

Éric Angelini, More Levenshtein distances, Personal blog, December 2023.

Cf. A118763, A367812, A367814, A367815.

a[1]=0;a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n-1],k]||EditDistance[ToString@a[n-1],ToString@k]!=3,k++];k);Array[a,72]

from itertools import islice
from Levenshtein import distance as Ld
def agen(): # generator of terms
    an, aset, mink = 0, {0}, 1
    while True:
        yield an
        s, k = str(an), mink
        while k in aset or Ld(s, str(k)) != 3: k += 1
        an = k
        aset.add(k)
        while mink in aset: mink += 1
print(list(islice(agen(), 72))) # Michael S. Branicky, Dec 01 2023

A367814 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 4.

Original entry on oeis.org

0, 1111, 2, 1000, 3, 1001, 4, 1002, 5, 1003, 6, 1004, 7, 1005, 8, 1006, 9, 1007, 21, 1008, 22, 1009, 23, 1010, 24, 1011, 25, 1012, 26, 1013, 27, 1014, 28, 1015, 29, 1016, 32, 1017, 33, 1018, 34, 1019, 35, 1020, 31, 1022, 36, 1021, 37, 1023, 38, 1024, 39, 1025, 41, 1026, 43, 1027, 44, 1028, 45, 1029, 46, 1030

Offset: 1

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

			a(1) =    0 and a(2) = 1111 are separated by an Ld of 4
a(2) = 1111 and a(3) =    2 are separated by an Ld of 4
a(3) =    2 and a(4) = 1000 are separated by an Ld of 4
a(4) = 1000 and a(5) =    3 are separated by an Ld of 4, etc.

Éric Angelini, More Levenshtein distances, Personal blog, December 2023.

Cf. A118763, A367812, A367813, A367815.

a[1]=0;a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n-1],k]||EditDistance[ToString@a[n-1],ToString@k]!=4,k++];k);Array[a,64]

from itertools import islice
from Levenshtein import distance as Ld
def agen(): # generator of terms
    an, aset, mink = 0, {0}, 1
    while True:
        yield an
        s, k = str(an), mink
        while k in aset or Ld(s, str(k)) != 4: k += 1
        an = k
        aset.add(k)
        while mink in aset: mink += 1
print(list(islice(agen(), 64))) # Michael S. Branicky, Dec 01 2023

A367815 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 5.

Original entry on oeis.org

0, 11111, 2, 10000, 3, 10001, 4, 10002, 5, 10003, 6, 10004, 7, 10005, 8, 10006, 9, 10007, 21, 10008, 22, 10009, 23, 10010, 24, 10011, 25, 10012, 26, 10013, 27, 10014, 28, 10015, 29, 10016, 32, 10017, 33, 10018, 34, 10019, 35, 10020, 31, 10022, 36, 10021, 37, 10023, 38, 10024, 39, 10025, 41, 10026, 43

Offset: 1

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

			a(1) =     0 and a(2) = 11111 are separated by an Ld of 5
a(2) = 11111 and a(3) = 1   2 are separated by an Ld of 5
a(3) =     2 and a(4) = 10000 are separated by an Ld of 5
a(4) = 10000 and a(5) =     3 are separated by an Ld of 5, etc.

Éric Angelini, More Levenshtein distances, Personal blog, December 2023.

Cf. A118763, A367812, A367813, A367814.

a[1]=0;a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n-1],k]||EditDistance[ToString@a[n-1],ToString@k]!=5,k++];k);Array[a,57]

from itertools import islice
from Levenshtein import distance as Ld
def agen(): # generator of terms
    an, aset, mink = 0, {0}, 1
    while True:
        yield an
        s, k = str(an), mink
        while k in aset or Ld(s, str(k)) != 5: k += 1
        an = k
        aset.add(k)
        while mink in aset: mink += 1
print(list(islice(agen(), 57))) # Michael S. Branicky, Dec 01 2023

cp's OEIS Frontend

A118764 Inverse of A118763.

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A118765 A118763(A118763(n)).

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A118767 Fixed points of permutations A118763, A118764, A118765 and A118766.

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A118768 First differences of A118763.

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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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A118766 A118764(A118764(n)).

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A367812 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 2.

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A367813 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 3.

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A367814 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 4.

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A367815 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 5.

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