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

1,1

Links

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

Formula

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

Example

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

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}]

Crossrefs

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

Sequence in context: A329455 A292808 A300813 * A014257 A247576 A339133

Adjacent sequences: A086351 A086352 A086353 * A086355 A086356 A086357

Keyword

base,easy,nonn

Author

Labos Elemer, Jul 21 2003

Status

approved