This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A202268 #33 Feb 15 2024 01:57:38
%S A202268 1,4,6,8,9,11,14,16,18,19,41,44,46,48,49,61,64,66,68,69,81,84,86,88,
%T A202268 89,91,94,96,98,99,111,114,116,118,119,141,144,146,148,149,161,164,
%U A202268 166,168,169,181,184,186,188,189,191,194,196,198,199,411,414,416,418,419
%N A202268 Numbers in which all digits are nonprimes (1, 4, 6, 8, 9).
%C A202268 Supersequence of A029581.
%C A202268 Subsequence of A084984.
%C A202268 If n-1 is represented as a zerofree base-5 number (see A084545) according to n-1=d(m)d(m-1)...d(3)d(2)d(1)d(0) then a(n) = Sum_{j=0..m} c(d(j))*10^j, where c(k)=1,4,6,8,9 for k=1..5. - _Hieronymus Fischer_, May 30 2012
%H A202268 Hieronymus Fischer, <a href="/A202268/b202268.txt">Table of n, a(n) for n = 1..10000</a>
%H A202268 Robert Baillie and Thomas Schmelzer, <a href="https://library.wolfram.com/infocenter/MathSource/7166/">Summing Kempner's Curious (Slowly-Convergent) Series</a>, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
%H A202268 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A202268 From _Hieronymus Fischer_, May 30 2012: (Start)
%F A202268 a(n) = Sum_{j=0..m-1} ((2*b_j(n)+1) mod 10 + floor((b_j(n)+4)/5) - floor((b_j(n)+1)/5))*10^j, where b_j(n))=floor((4*n+1-5^m)/(4*5^j)), m=floor(log_5(4*n+1)).
%F A202268 a(1*(5^n-1)/4) = 1*(10^n-1)/9.
%F A202268 a(2*(5^n-1)/4) = 4*(10^n-1)/9.
%F A202268 a(3*(5^n-1)/4) = 6*(10^n-1)/9.
%F A202268 a(4*(5^n-1)/4) = 8*(10^n-1)/9.
%F A202268 a(5*(5^n-1)/4) = 10^n-1.
%F A202268 a(n) = (10^log_5(4*n+1)-1)/9 for n=(5^k-1)/4, k>0.
%F A202268 a(n) <= 36/(9*2^log_5(9)-1)*(10^log_5(4*n+1)-1)/9 for n>0, equality holds for n=2.
%F A202268 a(n) > 0.776*10^log_5(4*n+1)-1)/9 for n>0.
%F A202268 a(n) >= A001742(n), equality holds for n=(5^k-1)/4, k>0.
%F A202268 a(n) = A084545(n) iff all digits of A084545(n) are 1, a(n)>A084545(n), else.
%F A202268 G.f.: g(x) = (x^(1/4)*(1-x))^(-1) Sum_{j>=0} 10^j*z(j)^(5/4)*(1-z(j))*(1 + 4z(j) + 6*z(j)^2 + 8*z(j)^3 + 9*z(j)^4)/(1-z(j)^5), where z(j)=x^5^j.
%F A202268 Also: g(x) = (1/(1-x))*(h_(5,0)(x) + 3h_(5,1)(x) + 2h_(5,2)(x) + 2h_(5,3)(x) + h_(5,4)(x) - 9*h_(5,5)(x)), where h_(5,k)(x) = Sum_{j>=0} 10^j*x^((5^(j+1)-1)/4)*(x^5^j)^k/(1-(x^5^j)^5). (End)
%F A202268 Sum_{n>=1} 1/a(n) = 2.897648425695540438556738520657902585305276107220152307051361916356295164643... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 15 2024
%e A202268 From _Hieronymus Fischer_, May 30 2012: (Start)
%e A202268 a(1000) = 14889.
%e A202268 a(10^4) = 498889
%e A202268 a(10^5) = 11188889.
%e A202268 a(10^6) = 446888889. (End)
%t A202268 Table[FromDigits/@Tuples[{1, 4, 6, 8, 9}, n], {n, 3}] // Flatten (* _Vincenzo Librandi_, Dec 17 2018 *)
%o A202268 (Magma) [n: n in [1..500] | Set(Intseq(n)) subset [1, 4, 6, 8, 9]]; // _Vincenzo Librandi_, Dec 17 2018
%Y A202268 Cf. A046034 (numbers in which all digits are primes), A001742 (numbers in which all digits are noncomposites excluding 0), A202267 (numbers in which all digits are noncomposites), A084984 (numbers in which all digits are nonprimes), A029581 (numbers in which all digits are composites).
%Y A202268 Cf. A084545, A001743, A001744, A014261, A014263.
%K A202268 nonn,base,easy
%O A202268 1,2
%A A202268 _Jaroslav Krizek_, Dec 25 2011