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 A259568 #29 Aug 28 2015 17:50:10 %S A259568 1,5,9,13,21,25,29,37,41,45,53,57,61,85,89,93,101,105,109,117,121,125, %T A259568 149,153,157,165,169,173,181,185,189,213,217,221,229,233,237,245,249, %U A259568 253,341,345,349,357,361,365,373,377,381,405,409,413,421,425,429,437,441,445,469,473,477,485,489,493,501,505,509,597,601,605 %N A259568 Numbers following gaps in the sequence of base-4 numbers that don't contain 0. %C A259568 Partial sums for the convergent modified harmonic series in base 4 excluding 0 = Sum of 1/a(n) + 1/(a(n) + 1) + 1/(a(n) + 2) = Sum of (3*a(n)^2 + 6*a(n) + 2)/(a(n)*(a(n) + 1)*(a(n) + 2)). %H A259568 Robert Baillie, <a href="http://dx.doi.org/10.2307/2321096">Sums of Reciprocals of Integers Missing a Given Digit</a>, American Mathematical Monthly (Washington, DC: Mathematical Association of America) 86 (5): 372-374, May 1979. doi:10.2307/2321096. ISSN 0002-9890. JSTOR 2321096. %e A259568 Pattern of numbers of skipped terms (numbers in base 4 with at least one zero) is 1 (4 = 10_4), 1 (8 = 20_4), 1 (12 = 30_4), 4+1 (16 = 100_4, 17 = 101_4, 18 = 102_4, 19 = 103_4, 20 = 110_4), 1, 1, 4+1, 1, 1, 4+1, 1, 1, 16+4+1, ... %o A259568 (PARI) lista(nn)=prec0 = 1; for(n=1, nn, if (vecmin(digits(n, 4)), if (prec0, print1(n,, ", ")); prec0 = 0, prec0 = 1);); \\ _Michel Marcus_, Aug 03 2015 %Y A259568 Subset of A016813 (congruent to 1 mod 4). a(n) = A023705(3n - 2). Each term is one more than the numbers that follow gaps in A196032. %K A259568 nonn,base,less %O A259568 1,2 %A A259568 _Sean Oneil_, Jun 30 2015