A130631 Multiplicative persistence of Fibonacci numbers.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 2, 2, 4, 1, 2, 3, 2, 2, 2, 1, 4, 2, 3, 1, 3, 3, 4, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1

Offset

0,10

Comments

From the 184th terms on all the Fibonacci numbers have some digits equal to zero (see A076564), thus their persistence is equal to 1.

Links

Table of n, a(n) for n=0..102.

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

a(n) = A031346(A000045(n)). - Michel Marcus, Feb 11 2025

Example

3524578 -> 3*5*2*4*5*7*8 = 33600 -> 3*3*6*0*0 = 0 -> persistence = 2.

Maple

P:=proc(n)local f0, f1, f2, i, k, w, ok, cont; f0:=0; f1:=1; print(0); print(0); for i from 0 by 1 to n do f2:=f1+f0; f0:=f1; f1:=f2; w:=1; ok:=1; k:=f2; if k<10 then print(0); else cont:=1; while ok=1 do while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w<10 then ok:=0; print(cont); else cont:=cont+1; k:=w; w:=1; fi; od; fi; od; end: P(100);

Mathematica

Table[Length[NestWhileList[Times@@IntegerDigits[#]&, Fibonacci[n], #>=10&]], {n, 0, 102}]-1 (* James C. McMahon, Feb 11 2025 *)

Crossrefs

Cf. A000045, A076564.

Sequence in context: A107901 A334236 A030423 * A282014 A390432 A241539

Adjacent sequences: A130628 A130629 A130630 * A130632 A130633 A130634

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 19 2007

Status

approved