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A217398 Numbers starting with 5.

%I A217398 #35 Jul 08 2025 10:46:12
%S A217398 5,50,51,52,53,54,55,56,57,58,59,500,501,502,503,504,505,506,507,508,
%T A217398 509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,
%U A217398 526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542
%N A217398 Numbers starting with 5.
%C A217398 The lower and upper asymptotic densities of this sequence are 1/45 and 5/27, respectively. - _Amiram Eldar_, Feb 27 2021
%C A217398 Also numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 5. - _Stefano Spezia_, Jul 08 2025
%H A217398 Jeremy Gardiner, <a href="/A217398/b217398.txt">Table of n, a(n) for n = 1..1111</a>
%H A217398 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A217398 A000030(a(n)) = 5; A143473(a(n)) = a(n). - _Reinhard Zumkeller_, Mar 13 2014
%F A217398 a(n) = n + (44*10^floor(log_10(9*n-8))-8)/9. - _Alan Michael Gómez Calderón_, May 17 2023
%t A217398 Select[Range[1000], IntegerDigits[#][[1]] == 5 &] (* _T. D. Noe_, Oct 02 2012 *)
%o A217398 (Haskell)
%o A217398 a217398 n = a217398_list !! (n-1)
%o A217398 a217398_list = filter ((== 5) . a000030) [1..]
%o A217398 -- _Reinhard Zumkeller_, Mar 13 2014
%o A217398 (Python)
%o A217398 def A217398(n): return n+(44*10**(len(str(9*n-8))-1))//9 # _Chai Wah Wu_, Dec 07 2024
%Y A217398 Cf. A000867, A011535.
%Y A217398 Subsequences include: A045711, A077330, A077681, A106415, A106425.
%Y A217398 Cf. A131835, A217394, A217395, A217397, A217399, A217400, A217401, A217402.
%K A217398 nonn,base,easy
%O A217398 1,1
%A A217398 _Jeremy Gardiner_, Oct 02 2012