A174025 -id:A174025 - cp's OEIS frontend

A003100 Decimal Gray code for n.

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

N. J. A. Sloane, Henry W. Gould

This permutation of the nonnegative integers is not self-inverse, as previously claimed. The first exception is a(100) = 190, but a(190) = 109. - Franklin T. Adams-Watters, Mar 05 2010

a(n) = A118757(n) for n<=100, = a(100)=A118757(100)=190, but a(101)=191, A118757(101)=180. - Reinhard Zumkeller, May 01 2006

M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 18.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Franklin T. Adams-Watters, Table of n, a(n) for n = 0..10000
A. J. Cole, Cyclic progressive number systems, Math. Gaz., 50 (1966), 122-131.
A. J. Cole, Cyclic progressive number systems, Math. Gaz., 50 (1966), 122-131. [Annotated scanned copy]
Henry W. Gould, Letters to N. J. A. Sloane, Oct 1973 and Jan 1974.
D. E. Knuth, Gray Codes (Vol. 4 of TAOCP)
Index entries for sequences that are permutations of the natural numbers

Inverse is A174025.

A003100 :=proc(n)
    local s,i:
    s:=[op(convert(n,base,10)),0]:
    add(piecewise(s[i+1] mod 2=0,s[i],9-s[i])*10^(i-1),i=1..nops(s)-1) :
end proc:
seq(A003100(j),j=0..100); # Pab Ter, Oct 14 2005

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 14 2005

Incorrect comment replaced by Franklin T. Adams-Watters, Mar 05 2010

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

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

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.

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A003100 Decimal Gray code for 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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A261729 Putative inverse of conjectured permutation in A261725.

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