A346007 Let b=5. If n == -i (mod b) for 0 <= i < b, then a(n) = binomial(b,i+1)*((n+i)/b)^(i+1).

0, 1, 5, 10, 10, 5, 32, 80, 80, 40, 10, 243, 405, 270, 90, 15, 1024, 1280, 640, 160, 20, 3125, 3125, 1250, 250, 25, 7776, 6480, 2160, 360, 30, 16807, 12005, 3430, 490, 35, 32768, 20480, 5120, 640, 40, 59049, 32805, 7290, 810, 45, 100000, 50000, 10000, 1000, 50

Offset: 0

Author

N. J. A. Sloane, Jul 25 2021

Keywords

• nonn

Comments

These are the numbers that would arise if the Moessner construction on page 64 of Conway-Guy's "Book of Numbers" were extended to the fifth powers.

References

• J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996. See pp. 63-64.

Crossrefs

Setting b = 2, 3, or 4 gives A346004, A346005, and A346006.

Cf. A125714, A346595.

Programs

Maple

f:=proc(n,b) local i;
for i from 0 to b-1 do
if ((n+i) mod b) = 0 then return(binomial(b,i+1)*((n+i)/b)^(i+1)); fi;
od;
end;
[seq(f(n,5),n=0..80)];

Python

from sympy import binomial
def A346007(n):
    i = (5-n)%5
    return binomial(5,i+1)*((n+i)//5)**(i+1) # Chai Wah Wu, Jul 25 2021