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