A325203 a(n) is 10^n represented in bijective base-9 numeration.

1, 11, 121, 1331, 14641, 162151, 1783661, 19731371, 228145181, 2519596991, 27726678111, 315994569221, 3477151372431, 38358665196741, 432956427275251, 4763631711137761, 53499948822526471, 588621548147792281, 6585837139636825191, 73555318547116177211

Offset

0,2

Comments

Differs from A055479 first at n = 7: a(7) = 19731371 < 20731371 = A055479(7).

Also: the (10^n)-th zeroless number. - M. F. Hasler, Jan 13 2020

Links

Alois P. Heinz, Table of n, a(n) for n = 0..954

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

Formula

a(n) = A052382(10^n) = A052382(A011557(n)).

Example

a(1) = 11_bij9   =                 1*9^1 + 1*9^0 =           9+1 =   10.
a(2) = 121_bij9  =         1*9^2 + 2*9^1 + 1*9^0 =       81+18+1 =  100.
a(3) = 1331_bij9 = 1*9^3 + 3*9^2 + 3*9^1 + 1*9^0 =  729+243+27+1 = 1000.
a(7) = 19731371_bij9 = 9*(9*(9*(9*(9*(9*(9*1+9)+7)+3)+1)+3)+7)+1 = 10^7.

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(10^n):
seq(a(n), n=0..23);

Prog

(PARI) A325203(n)=A052382(10^n) \\ M. F. Hasler, Jan 13 2020

Crossrefs

Cf. A011557, A052382 (zeroless numbers), A055479, A309908.

Sequence in context: A059734 A045582 A001020 * A055479 A195946 A003590

Adjacent sequences: A325200 A325201 A325202 * A325204 A325205 A325206

Keyword

nonn,base

Author

Alois P. Heinz, Sep 05 2019

Status

approved