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 A202267 #39 Feb 15 2024 01:57:16
%S A202267 0,1,2,3,5,7,10,11,12,13,15,17,20,21,22,23,25,27,30,31,32,33,35,37,50,
%T A202267 51,52,53,55,57,70,71,72,73,75,77,100,101,102,103,105,107,110,111,112,
%U A202267 113,115,117,120,121,122,123,125,127,130,131,132,133,135,137,150
%N A202267 Numbers in which all digits are noncomposites (1, 2, 3, 5, 7) or 0.
%C A202267 If n-1 is represented as a base-6 number (see A007092) 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)=0,1,2,3,5,7 for k=0..5. - _Hieronymus Fischer_, May 30 2012
%H A202267 Hieronymus Fischer, <a href="/A202267/b202267.txt">Table of n, a(n) for n = 1..10000</a>
%H A202267 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 A202267 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A202267 From _Hieronymus Fischer_, May 30 2012: (Start)
%F A202267 a(n) = (b_m(n)+1) mod 10 + floor((b_m(n)+2)/5) + floor((b_m(n)+1)/5) - 2*floor(b_m(n)/5))*10^m + sum_{j=0..m-1} (b_j(n) mod 6 + floor((b_j(n)+1)/6) + floor((b_j(n)+2)/6) - 2*floor(b_j(n)/6)))*10^j, where n>1, b_j(n)) = floor((n-1-6^m)/6^j), m = floor(log_6(n-1)).
%F A202267 a(1*6^n+1) = 1*10^n.
%F A202267 a(2*6^n+1) = 2*10^n.
%F A202267 a(3*6^n+1) = 3*10^n.
%F A202267 a(4*6^n+1) = 5*10^n.
%F A202267 a(5*6^n+1) = 7*10^n.
%F A202267 a(n) = 10^log_6(n-1) for n=6^k+1, k>0,
%F A202267 a(n) < 10^log_6(n-1) else.
%F A202267 a(n) = A007092(n-1) iff the digits of A007092(n-1) are <= 3, a(n)>A007092(n-1), else.
%F A202267 a(n) <= A084984(n), equality holds if the representation of n-1 as a base-6 number only has digits 0 or 1.
%F A202267 G.f.: g(x) = (x/(1-x))*sum_{j>=0} 10^j*x^6^j *(1-x^6^j)* (1 + 2x^6^j + 3(x^2)^6^j + 5(x^3)^6^j + 7(x^4)^6^j)/(1-x^6^(j+1)).
%F A202267 Also: g(x) = (x/(1-x))*(h_(6,1)(x) + h_(6,2)(x) + h_(6,3)(x) + 2*h_(6,4)(x) + 2*h_(6,5)(x) - 7*h_(6,6)(x)), where h_(6,k)(x) = sum_{j>=0} 10^j*x^(k*6^j)/(1-x^6^(j+1)). (End)
%F A202267 Sum_{n>=2} 1/a(n) = 4.945325883472729555972742252181522711968119529132581193614012706741310832798... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 15 2024
%e A202267 a(1000) = 5353.
%e A202267 a(10^4) = 115153
%e A202267 a(10^5) = 2070753.
%e A202267 a(10^6) = 33233353.
%t A202267 Union[Flatten[FromDigits/@Tuples[{0,1,2,3,5,7},3]]] (* _Harvey P. Dale_, Mar 11 2015 *)
%Y A202267 Supersequence of A001742 and A046034.
%Y A202267 Cf. A046034 (numbers in which all digits are primes), A001742 (numbers in which all digits are noncomposites excluding 0), A202268 (numbers in which all digits are nonprimes excluding 0), A084984 (numbers in which all digits are nonprimes), A029581 (numbers in which all digits are composites).
%Y A202267 Cf. A007092, A001743, A001744, A193238.
%K A202267 nonn,base,easy
%O A202267 1,3
%A A202267 _Jaroslav Krizek_, Dec 25 2011
%E A202267 Examples added by _Hieronymus Fischer_, May 30 2012