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

Author

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

Keywords

• nonn
• base
• easy
• look

Comments

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

References

• 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).

Links

• 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

Crossrefs

Inverse is A174025.

Programs

Maple

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

Extensions

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

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