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A301729 a(0)=1; thereafter positive numbers that are congruent to {0, 1, 3, 5} mod 6.

%I A301729 #16 Dec 31 2021 05:47:25
%S A301729 1,1,3,5,6,7,9,11,12,13,15,17,18,19,21,23,24,25,27,29,30,31,33,35,36,
%T A301729 37,39,41,42,43,45,47,48,49,51,53,54,55,57,59,60,61,63,65,66,67,69,71,
%U A301729 72,73,75,77,78,79,81,83,84,85,87,89,90,91,93,95,96,97
%N A301729 a(0)=1; thereafter positive numbers that are congruent to {0, 1, 3, 5} mod 6.
%H A301729 A. V. Shutov, <a href="http://mi.mathnet.ru/eng/znsl933">The number of words of a given length in the planar crystallographic groups</a>, (in Russian), Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), Vol. 302 (2003), Anal. Teor. Chisel i Teor. Funkts. 19, pp. 188-197, 203; <a href="https://doi.org/10.1007/s10958-005-0329-2">translation</a>, in J. Math. Sci. (N.Y.), Vol. 129, No. 3 (2005), pp. 3922-3926 [MR2023041]. See Table 1, line "p31m".
%F A301729 Sum_{n>=1} (-1)^(n+1)/a(n) = log(108)/6 = log(2)/3 + log(3)/2. - _Amiram Eldar_, Dec 31 2021
%p A301729 f:= proc(n) if n=0 then 1
%p A301729 elif (n mod 4) = 0 then (3*n)/2
%p A301729 elif (n mod 4) = 1 then (3*n-1)/2
%p A301729 elif (n mod 4) = 2 then (3*n)/2
%p A301729 else (3*n+1)/2 fi;
%p A301729 end;
%p A301729 s1 := [seq(f(n),n=0..70)];
%t A301729 Join[{1}, Select[Range[100], MemberQ[{0, 1, 3, 5}, Mod[#,6]] &]] (* _Amiram Eldar_, Dec 31 2021 *)
%Y A301729 Essentially the same as A047273.
%K A301729 nonn
%O A301729 0,3
%A A301729 _N. J. A. Sloane_, Mar 30 2018