A089600 Another lazy binary representation of n: similar to A089591 except that the single carry is performed before the increment instead of after.

0, 1, 2, 11, 12, 21, 102, 111, 112, 121, 202, 211, 1012, 1021, 1102, 1111, 1112, 1121, 1202, 1211, 2012, 2021, 2102, 2111, 10112, 10121, 10202, 10211, 11012, 11021, 11102, 11111, 11112, 11121, 11202, 11211, 12012, 12021, 12102, 12111, 20112

Offset

0,3

Links

Table of n, a(n) for n=0..40.

Formula

Let b(n) = A089591(n). Then a(0) = b(0) = 0; b(n) = if n is odd then b((n-1)/2):1 else a(n/2):0; a(n) = if n is odd then a((n-1)/2):1 else b(n/2-1):2.

Maple

A089591 := proc(n) option remember ; local nhalf ; if n <= 1 then RETURN(n) ; else nhalf := floor(n/2) ; if n mod 2 = 1 then RETURN(10*A089591(nhalf) +1) ; else RETURN(10*(A089591(nhalf-1)+1)) ; fi ; fi ; end: A089600 := proc(n) option remember ; local nhalf ; nhalf := floor(n/2) ; if n <= 1 then RETURN(n) ; else if n mod 2 = 1 then RETURN(10*A089600(nhalf) +1) ; else RETURN(10*A089591(nhalf-1)+2) ; fi ; fi ; end: for n from 0 to 200 do printf("%d, ", A089600(n)) ; od ; # R. J. Mathar, Mar 11 2007

Crossrefs

Sequence in context: A053880 A063112 A038113 * A114034 A136970 A136967

Adjacent sequences: A089597 A089598 A089599 * A089601 A089602 A089603

Keyword

nonn,easy,base

Author

Jeff Erickson, Dec 31 2003

Extensions

More terms from R. J. Mathar, Mar 11 2007

Status

approved