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A178501 Zero followed by powers of ten.

%I A178501 #50 Jul 23 2025 00:59:58
%S A178501 0,1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000,
%T A178501 10000000000,100000000000,1000000000000,10000000000000,
%U A178501 100000000000000,1000000000000000,10000000000000000,100000000000000000,1000000000000000000,10000000000000000000,100000000000000000000
%N A178501 Zero followed by powers of ten.
%C A178501 The sequence S consisting of the nonnegative numbers arranged in lexicographic order according to their decimal expansion begins 0, 1, 10, 100, 1000, ..., 2, 20, 200, 2000, ..., 3, 30, ... does not have an OEIS entry, since there are uncountably many terms before 2 appears (or even before 100000010000 appears). However, S does begin with the present sequence. - _N. J. A. Sloane_, Dec 09 2024
%C A178501 a(n)^k + reverse(a(n))^k is a palindrome for any positive integer k. - _Bui Quang Tuan_, Mar 31 2015
%H A178501 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).
%F A178501 a(n+1) = A011557(n).
%F A178501 a(n) = A178500(n)/10.
%F A178501 From _Paul Barry_, Jul 09 2003: (Start)
%F A178501 a(n) = (10^n - 0^n)/10.
%F A178501 E.g.f.: exp(5*x)*sinh(5*x)/5.
%F A178501 Binomial transform of A015577. (End)
%F A178501 G.f.: x/(1 - 10*x). - _Chai Wah Wu_, Jun 17 2020
%F A178501 From _Elmo R. Oliveira_, Jul 21 2025: (Start)
%F A178501 a(n) = 10*a(n-1) for n > 1.
%F A178501 a(n) = A093136(n)/2 for n >= 1. (End)
%t A178501 Join[{0}, 10^Range[0, 19]] (* _Alonso del Arte_, Mar 31 2015 *)
%o A178501 (PARI) a(n)=10^n\10 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A178501 (PARI) concat(0, Vec(-x/(10*x-1) + O(x^22))) \\ _Elmo R. Oliveira_, Jul 21 2025
%Y A178501 Cf. A093136, A131577, A140429, A178500; subsequence of A029793.
%Y A178501 The powers of 10, A011557, is a subsequence.
%K A178501 nonn,easy
%O A178501 0,3
%A A178501 _Reinhard Zumkeller_, May 28 2010
%E A178501 More terms from _Elmo R. Oliveira_, Jul 21 2025