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A101305 Begin with 0 and at each successive iteration append the next power of 10.

%I A101305 #34 Aug 06 2025 22:36:55
%S A101305 0,10,10100,101001000,10100100010000,10100100010000100000,
%T A101305 101001000100001000001000000,10100100010000100000100000010000000,
%U A101305 10100100010000100000100000010000000100000000,101001000100001000001000000100000001000000001000000000
%N A101305 Begin with 0 and at each successive iteration append the next power of 10.
%H A101305 Harvey P. Dale, <a href="/A101305/b101305.txt">Table of n, a(n) for n = 0..43</a>
%e A101305 a(1) = 10;
%e A101305 a(2) = 10100 (concatenate 10 and 100);
%e A101305 a(3) = 101001000 (concatenate 10, 100 and 1000);
%e A101305 a(4) = 10100100010000.
%t A101305 f[n_] := FromDigits[ Flatten[ Table[ IntegerDigits[10^i], {i, n}]]]; Table[ f[n], {n, 8}] (* _Robert G. Wilson v_, Dec 22 2004 *)
%t A101305 nxt[{n_,a_}]:={n+1,FromDigits[Join[IntegerDigits[a],IntegerDigits[ 10^(n+1)]]]}; NestList[nxt,{0,0},10][[All,2]] (* _Harvey P. Dale_, Oct 26 2020 *)
%o A101305 (Python)
%o A101305 def a(n): return 0 if n==0 else int("".join("1"+"0"*(i+1) for i in range(n)))
%o A101305 print([a(n) for n in range(10)]) # _Michael S. Branicky_, Jun 28 2022
%o A101305 (Python)
%o A101305 def A101305(n): return 10**n*sum(10**(k*((n<<1)-k+1)>>1) for k in range(n)) # _Chai Wah Wu_, Aug 05 2025
%Y A101305 Cf. A011557, A104462.
%K A101305 nonn,base
%O A101305 0,2
%A A101305 _Jorge Coveiro_, Dec 22 2004
%E A101305 Edited by _Robert G. Wilson v_, Dec 22 2004