A118761 -id:A118761 - cp's OEIS frontend

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

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

A102491 Numbers whose base-20 representation can be written with decimal digits.

Original entry on oeis.org

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, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 120, 121, 122, 123, 124, 125, 126

Offset: 1

Reinhard Zumkeller, Jan 12 2005

a(n) = A118761(n) for n<=50. - Reinhard Zumkeller, May 01 2006

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Vigesimal
Wikipedia, Vigesimal

Complement of A102492; Cf. A102487, A102489, A102493. Cf. A037454, A037462, A007091.

import Data.List (unfoldr)
a102491 n = a102491_list !! (n-1)
a102491_list = filter (all (<= 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 20)) [0..]
-- Reinhard Zumkeller, Jun 27 2013

seq(n + (1/2)*add(20^k*floor(n/10^k), k = 1..floor(ln(n)/ln(10))), n = 1..100); # Peter Bala, Dec 01 2016

Select[Range@ 126, Total@ Take[Most@ DigitCount[#, 20], -10] == 0 &] (* Michael De Vlieger, Apr 09 2016 *)

isok(n) = (n==0) || ((d=digits(n, 20)) && (vecmax(d) < 10)); \\ Michel Marcus, Apr 09 2016

a(n) = fromdigits(digits(n-1),20) \\ Ruud H.G. van Tol, Dec 08 2022

A102491_list = [int(str(x), 20) for x in range(10**6)] # Chai Wah Wu, Apr 09 2016

From Peter Bala, Dec 01 2016: (Start)
If n = Sum_{i = 0..m} d(i)*10^i is the decimal expansion of n then a(n+1) = Sum_{i = 0..m} d(i)*20^i.
a(n+1) = n + 1/2*Sum_{k >= 1} 20^k*floor(n/10^k). Cf. A037454, A037462 and A007091.
a(1) = 0; a(n+1) = 20*a(n/10+1) if n == 0 (mod 10) else a(n+1) = a(n) + 1. (End)
G.f. g(x) satisfies g(x) = 20*Sum_{1<=k<=9} x^k*g(x^10)/x^9 + Sum_{1<=k<=9} k*x^(k+1)/(1-x^10). - Robert Israel, Dec 01 2016

A118758 Inverse of A118757.

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

Permutation of the natural numbers with fixed points A118761: a(A118761(n)) = A118761(n);

A118760(n) = a(a(n)); a(n) = A118757(n) for n < 100.

Cf. A118764.

A024657 n written in fractional base 10/2.

Original entry on oeis.org

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, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 220, 221, 222, 223, 224, 225, 226, 227

Offset: 0

David W. Wilson

To represent a number in base b, if a digit exceeds b-1, subtract b and carry 1. In fractional base a/b, subtract a and carry b.

Also numbers which are written the same in base 20/2 as in base 10. The sequence consists of numbers which have digits in {0,2,4,6,8} except that the unit digit can be any from {0,1,2,3,4,5,6,7,8,9} - Henry Bottomley, Nov 17 2000

Amiram Eldar, Table of n, a(n) for n = 0..10000
Index entries for sequences related to fractional bases.

Cf. A007091, A058185, A058186, A102491, A118761.

a[n_] := a[n] = If[n == 0, 0, 10 * a[2 * Floor[n/10]] + Mod[n, 10]]; Array[a, 50, 0] (* Amiram Eldar, Aug 02 2025 *)

a(n) = if(n == 0, 0, 10 * a(n\10 * 2) + n % 10); \\ Amiram Eldar, Aug 02 2025

a(n) = A118761(n+1) for n < 50. - Reinhard Zumkeller, May 01 2006

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.

cp's OEIS Frontend

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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A102491 Numbers whose base-20 representation can be written with decimal digits.

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A118758 Inverse of A118757.

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A024657 n written in fractional base 10/2.

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

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