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A217399 Numbers starting with 6.

%I A217399 #38 Dec 07 2024 11:10:37
%S A217399 6,60,61,62,63,64,65,66,67,68,69,600,601,602,603,604,605,606,607,608,
%T A217399 609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,
%U A217399 626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642
%N A217399 Numbers starting with 6.
%C A217399 The lower and upper asymptotic densities of this sequence are 1/54 and 10/63, respectively. - _Amiram Eldar_, Feb 27 2021
%H A217399 Jeremy Gardiner, <a href="/A217399/b217399.txt">Table of n, a(n) for n = 1..1111</a>
%H A217399 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A217399 a(n) = n + (53*10^floor(log_10(9*n-8))-8)/9. - _Alan Michael Gómez Calderón_, May 17 2023
%p A217399 seq(seq(6*10^n+k, k=0..10^n-1),n=0..3); # _Robert Israel_, May 08 2017
%t A217399 Select[Range[1000], IntegerDigits[#][[1]] == 6 &] (* _T. D. Noe_, Oct 02 2012 *)
%o A217399 (PARI) isok(n) = digits(n)[1] == 6; \\ _Michel Marcus_, May 08 2017
%o A217399 (GAP) Flat(List([0..2],n->List([0..10^n-1],k->6*10^n+k))); # _Muniru A Asiru_, Nov 21 2018
%o A217399 (Magma) [n: n in [1..1600] | Intseq(n)[#Intseq(n)] eq 6]; // _Vincenzo Librandi_, Nov 24 2018
%o A217399 (Python)
%o A217399 def A217399(n): return n+(53*10**(len(str(9*n-8))-1))//9 # _Chai Wah Wu_, Dec 07 2024
%Y A217399 Cf. A000870, A011536.
%Y A217399 Subsequences include: A045712, A077331, A077682, A106416, A106426.
%Y A217399 Cf. A131835, A217394, A217395, A217397, A217398, A217400, A217401, A217402.
%K A217399 nonn,base,easy
%O A217399 1,1
%A A217399 _Jeremy Gardiner_, Oct 02 2012