A084675 Product of the first n digits of the Golden Ratio phi = 1.6180339... (treating 0's as if they were 1's).

1, 6, 6, 48, 48, 144, 432, 3888, 31104, 248832, 1741824, 6967296, 62705664, 501645312, 4514807808, 18059231232, 144473849856, 577895399424, 4623163195392, 9246326390784, 9246326390784, 36985305563136

Offset: 1

Author

Cino Hilliard, Jun 29 2003

Keywords

• easy
• nonn
• base

Crossrefs

Cf. A074850.

Programs

Maple

Digits:=100: Phi:= (sqrt(5)+1)/2: A084675:=proc(n) options remember: local d: d:=trunc(10*frac(Phi*10^(n-2))): if n=1 then RETURN(d) else RETURN(A084675(n-1)*piecewise(d<>0,d,1)) fi: end; seq(A084675(n),n=1..25); (C. Ronaldo)

Mathematica

FoldList[Times,(RealDigits[GoldenRatio,10,30][[1]]/.(0->1))] (* Harvey P. Dale, Jun 11 2016 *)

PARI

phitorial(n) = { default(realprecision,10000); p = (sqrt(5)+1)/20; default(realprecision,28); for(j=1,n, eitor=1; e1=p; for(x=1,j, d = e1*10; d1=floor(d); if(d1<>0,eitor*=d1); e1 = frac(d); ); print1(eitor",") ) }

Formula

Phi = (sqrt(5)+1)/2 = 1.618033988749894848204586834...

Extensions

Definition clarified by Harvey P. Dale, Jun 11 2016.