A325203 - OEIS

%I #37 Feb 10 2020 21:43:18

%S 1,11,121,1331,14641,162151,1783661,19731371,228145181,2519596991,

%T 27726678111,315994569221,3477151372431,38358665196741,

%U 432956427275251,4763631711137761,53499948822526471,588621548147792281,6585837139636825191,73555318547116177211

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

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

%C Also: the (10^n)-th zeroless number. - _M. F. Hasler_, Jan 13 2020

%H Alois P. Heinz, <a href="/A325203/b325203.txt">Table of n, a(n) for n = 0..954</a>

%H R. R. Forslund, <a href="http://www.emis.de/journals/SWJPAM/Vol1_1995/rrf01.ps">A logical alternative to the existing positional number system</a>, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Zerofree.html">Zerofree</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bijective_numeration">Bijective numeration</a>

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

%e a(1) = 11_bij9   =                 1*9^1 + 1*9^0 =           9+1 =   10.

%e a(2) = 121_bij9  =         1*9^2 + 2*9^1 + 1*9^0 =       81+18+1 =  100.

%e a(3) = 1331_bij9 = 1*9^3 + 3*9^2 + 3*9^1 + 1*9^0 =  729+243+27+1 = 1000.

%e a(7) = 19731371_bij9 = 9*(9*(9*(9*(9*(9*(9*1+9)+7)+3)+1)+3)+7)+1 = 10^7.

%p b:= proc(n) local d, l, m; m:= n; l:= "";

%p       while m>0 do d:= irem(m, 9, 'm');

%p         if d=0 then d:=9; m:= m-1 fi; l:= d, l

%p       od; parse(cat(l))

%p     end:

%p a:= n-> b(10^n):

%p seq(a(n), n=0..23);

%o (PARI) A325203(n)=A052382(10^n) \\ _M. F. Hasler_, Jan 13 2020

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

%K nonn,base

%O 0,2

%A _Alois P. Heinz_, Sep 05 2019