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Successive numbers arising from the Moessner construction of the cubes on page 64 of Conway-Guy's "Book of Numbers".
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%I #13 Jul 27 2021 06:22:15

%S 0,1,3,3,8,12,6,27,27,9,64,48,12,125,75,15,216,108,18,343,147,21,512,

%T 192,24,729,243,27,1000,300,30,1331,363,33,1728,432,36,2197,507,39,

%U 2744,588,42,3375,675,45,4096,768,48,4913,867,51,5832,972,54,6859,1083,57,8000,1200

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

%C a(3*k+1) = (k+1)^3 for k >= 0.

%D 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 a(n) = n if n mod 3 = 0, = ((n+2)/3)^3 if n mod 3 = 1, and otherwise (n+1)^2/3.

%p f:=proc(n) if (n mod 3) = 0 then n

%p elif (n mod 3) = 1 then ((n+2)/3)^3;

%p else (n+1)^2/3; fi; end;

%p [seq(f(n),n=0..100)];

%o (Python)

%o 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 Cf. A125714, A346004, A346006-A346007, A346595.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jul 25 2021