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A386552 Concatenate powers of 10.

%I A386552 #28 Aug 06 2025 01:04:01
%S A386552 1,110,110100,1101001000,110100100010000,110100100010000100000,
%T A386552 1101001000100001000001000000,110100100010000100000100000010000000,
%U A386552 110100100010000100000100000010000000100000000,1101001000100001000001000000100000001000000001000000000
%N A386552 Concatenate powers of 10.
%C A386552 Binary version of A045507. Base-2 representation of A164894.
%C A386552 Concatenate first A000217(n+1) terms of A010054.
%H A386552 Jason Bard, <a href="/A386552/b386552.txt">Table of n, a(n) for n = 0..43</a>
%F A386552 a(n) = Sum_{k=1..n+1} 10^A133082(k,n+2).
%F A386552 a(n) = A101305(n) + 10^A000096(n).
%F A386552 For n >= 1, a(n) = 10^(n+1)*a(n-1)+10^n.
%F A386552 Number of digits in a(n) is A000217(n+1).
%p A386552 a:= proc(n) option remember;
%p A386552       `if`(n<0, 0, parse(cat(a(n-1), 10^n)))
%p A386552     end:
%p A386552 seq(a(n), n=0..10);  # _Alois P. Heinz_, Jul 28 2025
%t A386552 a[0] = 1; a[n_] := a[n - 1]*10^(n+1) + 10^n; Table[a[n], {n, 0, 9}]
%o A386552 (Python)
%o A386552 def A386552(n): return 10**n*sum(10**(k*((n<<1)-k+1)>>1) for k in range(n+1)) # _Chai Wah Wu_, Aug 05 2025
%Y A386552 Cf. A000096, A000217, A010054, A011557, A045507, A051639, A101305, A133082, A164894, A242646.
%K A386552 nonn,base,easy
%O A386552 0,2
%A A386552 _Jason Bard_, Jul 25 2025