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A301729
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a(0)=1; thereafter positive numbers that are congruent to {0, 1, 3, 5} mod 6.
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2
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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, 37, 39, 41, 42, 43, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 63, 65, 66, 67, 69, 71, 72, 73, 75, 77, 78, 79, 81, 83, 84, 85, 87, 89, 90, 91, 93, 95, 96, 97
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OFFSET
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0,3
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LINKS
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A. V. Shutov, The number of words of a given length in the planar crystallographic groups, (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; translation, in J. Math. Sci. (N.Y.), Vol. 129, No. 3 (2005), pp. 3922-3926 [MR2023041]. See Table 1, line "p31m".
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FORMULA
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Sum_{n>=1} (-1)^(n+1)/a(n) = log(108)/6 = log(2)/3 + log(3)/2. - Amiram Eldar, Dec 31 2021
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MAPLE
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f:= proc(n) if n=0 then 1
elif (n mod 4) = 0 then (3*n)/2
elif (n mod 4) = 1 then (3*n-1)/2
elif (n mod 4) = 2 then (3*n)/2
else (3*n+1)/2 fi;
end;
s1 := [seq(f(n), n=0..70)];
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MATHEMATICA
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Join[{1}, Select[Range[100], MemberQ[{0, 1, 3, 5}, Mod[#, 6]] &]] (* Amiram Eldar, Dec 31 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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