A073637 Digital root (cf. A010888) of prime(n)^3.

8, 9, 8, 1, 8, 1, 8, 1, 8, 8, 1, 1, 8, 1, 8, 8, 8, 1, 1, 8, 1, 1, 8, 8, 1, 8, 1, 8, 1, 8, 1, 8, 8, 1, 8, 1, 1, 1, 8, 8, 8, 1, 8, 1, 8, 1, 1, 1, 8, 1, 8, 8, 1, 8, 8, 8, 8, 1, 1, 8, 1, 8, 1, 8, 1, 8, 1, 1, 8, 1, 8, 8, 1, 1, 1, 8, 8, 1, 8, 1, 8, 1, 8, 1, 1, 8, 8, 1, 8, 1, 8, 8, 1, 8, 1, 8, 8, 8, 1, 1

Offset: 1

Author

Zak Seidov, Sep 01 2002, Oct 23 2009

Keywords

• nonn
• base

Comments

Apart from a(2)=9 all other terms are either 1 or 8.

Examples

			a(3)=8 because p(3)=5 and 5^3=125 -> sum-of-digits = 8. a(4)=1 because p(3)=7 and 7^3=343 -> sum-of-digits = 10 -> sum-of-digits = 1.
		

Crossrefs

Cf. A010888, A021596, A056992, A010888, A038194, A166923.

Programs

Mathematica

n=3; su[x_] := Sum[IntegerDigits[x][[i]], {i, Length[IntegerDigits[x]]}]; Table[su[su[su[su[Prime[x]^n]]]], {x, 100}]
Table[If[(m9=Mod[Prime[n]^3,9])==0,9,m9],{n,200}]

Extensions

Edited by N. J. A. Sloane, Oct 29 2009