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 A259566 #36 Oct 13 2023 14:20:17 %S A259566 1,4,7,13,16,22,25,40,43,49,52,67,70,76,79,121,124,130,133,148,151, %T A259566 157,160,202,205,211,214,229,232,238,241,364,367,373,376,391,394,400, %U A259566 403,445,448,454,457,472,475,481,484,607,610,616,619,634,637,643,646,688,691,697,700,715,718,724,727,1093,1096,1102,1105,1120 %N A259566 Numbers following gaps in the sequence of base-3 numbers that don't contain 0. %C A259566 Partial sums for the convergent modified harmonic series in base 3 excluding 0 = Sum of 1/a(n) + 1/(a(n) + 1) = Sum of (2*a(n) + 1)/(a(n)*(a(n) + 1)). %H A259566 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. %F A259566 a(n) = A032924(2n - 1). %e A259566 Pattern of numbers of skipped terms (numbers in base 3 with at least one zero) is 1 (3 = 10_3), 1 (6 = 20_3), 3+1 (9 = 100_3, 10 = 101_3, 11 = 102_3, 12 = 110_3), 1, 3+1, 1, 9+3+1, 1, 3+1, 1, 9+3+1, 1, 3+1, 1, 27+9+3+1, ... %o A259566 (PARI) lista(nn)=prec0 = 1; for(n=1, nn, if (vecmin(digits(n, 3)), if (prec0, print1(n,, ", ")); prec0 = 0, prec0 = 1);); \\ _Michel Marcus_, Aug 03 2015 %o A259566 (Python) %o A259566 def A259566(n): return int(bin(m:=n)[3:],3)*3 + (3**m.bit_length()-1>>1) if n>1 else 1 # _Chai Wah Wu_, Oct 13 2023 %Y A259566 Cf. A032924. %Y A259566 Subset of A016777 (congruent to 1 mod 3). %Y A259566 Each term is one more than each number that follows a gap in A081605. %K A259566 nonn,base,less %O A259566 1,2 %A A259566 _Sean Oneil_, Jun 30 2015