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

Author

Jeff Erickson, Dec 31 2003

Keywords

• nonn
• easy
• base

Programs

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

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.

Extensions

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