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A346005 Successive numbers arising from the Moessner construction of the cubes on page 64 of Conway-Guy's "Book of Numbers".

%I A346005 #13 Jul 27 2021 06:22:15
%S A346005 0,1,3,3,8,12,6,27,27,9,64,48,12,125,75,15,216,108,18,343,147,21,512,
%T A346005 192,24,729,243,27,1000,300,30,1331,363,33,1728,432,36,2197,507,39,
%U A346005 2744,588,42,3375,675,45,4096,768,48,4913,867,51,5832,972,54,6859,1083,57,8000,1200
%N A346005 Successive numbers arising from the Moessner construction of the cubes on page 64 of Conway-Guy's "Book of Numbers".
%C A346005 a(3*k+1) = (k+1)^3 for k >= 0.
%D A346005 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996. Sequence can be seen in the successive circled numbers at the top of page 64.
%F A346005 a(n) = n if n mod 3 = 0, = ((n+2)/3)^3 if n mod 3 = 1, and otherwise (n+1)^2/3.
%p A346005 f:=proc(n) if (n mod 3) = 0 then n
%p A346005 elif (n mod 3) = 1 then ((n+2)/3)^3;
%p A346005 else (n+1)^2/3; fi; end;
%p A346005 [seq(f(n),n=0..100)];
%o A346005 (Python)
%o A346005 def A346005(n): return n if n % 3 == 0 else ((n+2)//3)**3 if n % 3 == 1 else (n+1)**2//3 # _Chai Wah Wu_, Jul 25 2021
%Y A346005 Cf. A125714, A346004, A346006-A346007, A346595.
%K A346005 nonn
%O A346005 0,3
%A A346005 _N. J. A. Sloane_, Jul 25 2021