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%I #29 Aug 28 2015 17:50:10
%S 1,5,9,13,21,25,29,37,41,45,53,57,61,85,89,93,101,105,109,117,121,125,
%T 149,153,157,165,169,173,181,185,189,213,217,221,229,233,237,245,249,
%U 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 Numbers following gaps in the sequence of base-4 numbers that don't contain 0.
%C 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 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 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 (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 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 nonn,base,less
%O 1,2
%A _Sean Oneil_, Jun 30 2015
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