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

%I A309908 #26 Feb 16 2025 08:33:56
%S A309908 1,2,4,8,17,35,71,152,314,628,1357,2725,5551,12212,24424,48848,98797,
%T A309908 218715,438531,878162,1867334,3845668,7792447,16694895,34499911,
%U A309908 69121922,149243944,299487988,619987187,1342185385,2684381781,5478773672,11968657454,24148425918
%N A309908 a(n) is 2^n represented in bijective base-9 numeration.
%C A309908 Differs from A001357 first at n = 16: a(16) = 98797 < 108807 = A001357(16).
%H A309908 Alois P. Heinz, <a href="/A309908/b309908.txt">Table of n, a(n) for n = 0..1000</a>
%H A309908 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 A309908 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Zerofree.html">Zerofree</a>
%H A309908 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bijective_numeration">Bijective numeration</a>
%F A309908 a(n) = A052382(2^n) = A052382(A000079(n)).
%e A309908 a(10) =  1357_bij9 =       9*(9*(9*1+3)+5)+7 =  1024 = 2^10.
%e A309908 a(16) = 98797_bij9 = 9*(9*(9*(9*9+8)+7)+9)+7 = 65536 = 2^16.
%p A309908 b:= proc(n) local d, l, m; m:= n; l:= "";
%p A309908       while m>0 do d:= irem(m, 9, 'm');
%p A309908         if d=0 then d:=9; m:= m-1 fi; l:= d, l
%p A309908       od; parse(cat(l))
%p A309908     end:
%p A309908 a:= n-> b(2^n):
%p A309908 seq(a(n), n=0..33);
%Y A309908 Cf. A000079, A001357, A047855, A052382, A093135, A214676, A325203.
%K A309908 nonn,base
%O A309908 0,2
%A A309908 _Alois P. Heinz_, Aug 21 2019