A086354 Fixed point if (nonzero-digit product)-function at initial value 2^n is iterated.

2, 4, 8, 6, 6, 8, 6, 6, 1, 8, 8, 2, 6, 2, 2, 4, 8, 2, 1, 6, 2, 2, 6, 8, 2, 8, 2, 8, 2, 2, 8, 6, 6, 2, 2, 6, 2, 2, 6, 8, 8, 6, 3, 4, 2, 2, 6, 6, 2, 8, 6, 2, 2, 9, 8, 6, 6, 5, 8, 2, 8, 8, 2, 6, 2, 8, 8, 8, 5, 8, 8, 8, 2, 8, 6, 4, 8, 6, 2, 7, 1, 8, 8, 4, 2, 8, 8

Offset: 1

Author

Labos Elemer, Jul 21 2003

Keywords

• base
• easy
• nonn

Examples

			n=20, 2^20=1048576, iteration list={1048576,6720,84,32,6}, so a(20)=6.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051801, A051802, A086353-A086361, A029898, A010888.

Programs

Maple

A051801 := proc(n) local d,j: d:=convert(n,base,10): return mul(`if`(d[j]=0,1,d[j]), j=1..nops(d)): end: A086354 := proc(n) local m: m:=2^n: while(length(m)>1)do m:=A051801(m): od: return m: end: seq(A086354(n),n=1..100); # Nathaniel Johnston, May 04 2011

Mathematica

prd[x_] := Apply[Times, DeleteCases[IntegerDigits[x], 0]] Table[FixedPoint[prd, 2^w], {w, 1, 128}]

Formula

a(n) = A051802(2^n) = fixed point of A051801(2^n).