A309908 a(n) is 2^n represented in bijective base-9 numeration.

1, 2, 4, 8, 17, 35, 71, 152, 314, 628, 1357, 2725, 5551, 12212, 24424, 48848, 98797, 218715, 438531, 878162, 1867334, 3845668, 7792447, 16694895, 34499911, 69121922, 149243944, 299487988, 619987187, 1342185385, 2684381781, 5478773672, 11968657454, 24148425918

Offset: 0

Author

Alois P. Heinz, Aug 21 2019

Keywords

• nonn
• base

Comments

Differs from A001357 first at n = 16: a(16) = 98797 < 108807 = A001357(16).

Examples

			a(10) =  1357_bij9 =       9*(9*(9*1+3)+5)+7 =  1024 = 2^10.
a(16) = 98797_bij9 = 9*(9*(9*(9*9+8)+7)+9)+7 = 65536 = 2^16.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• R. R. Forslund, A logical alternative to the existing positional number system, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.
• Eric Weisstein's World of Mathematics, Zerofree
• Wikipedia, Bijective numeration

Crossrefs

Cf. A000079, A001357, A047855, A052382, A093135, A214676, A325203.

Programs

Maple

b:= proc(n) local d, l, m; m:= n; l:= "";
      while m>0 do d:= irem(m, 9, 'm');
        if d=0 then d:=9; m:= m-1 fi; l:= d, l
      od; parse(cat(l))
    end:
a:= n-> b(2^n):
seq(a(n), n=0..33);

Formula

a(n) = A052382(2^n) = A052382(A000079(n)).