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

0, 1, 3, 3, 8, 12, 6, 27, 27, 9, 64, 48, 12, 125, 75, 15, 216, 108, 18, 343, 147, 21, 512, 192, 24, 729, 243, 27, 1000, 300, 30, 1331, 363, 33, 1728, 432, 36, 2197, 507, 39, 2744, 588, 42, 3375, 675, 45, 4096, 768, 48, 4913, 867, 51, 5832, 972, 54, 6859, 1083, 57, 8000, 1200

Offset: 0

Author

N. J. A. Sloane, Jul 25 2021

Keywords

• nonn

Comments

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

References

• 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.

Crossrefs

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

Programs

Maple

f:=proc(n) if (n mod 3) = 0 then n
elif (n mod 3) = 1 then ((n+2)/3)^3;
else (n+1)^2/3; fi; end;
[seq(f(n),n=0..100)];

Python

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

Formula

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