A131838 Multiplicative persistence of Woodall numbers.

0, 0, 1, 2, 3, 3, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 5, 2, 2, 1, 1, 8, 3, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 20 2007

Keywords

• easy
• nonn
• base

Comments

After the 111th term, all the numbers have some digits equal to zero, thus the persistence is equal to 1.

Examples

			Woodall number 159 --> 1*5*9=45 --> 4*5=20 --> 2*0=0 thus persistence is 3.
		

Crossrefs

Cf. A003261, A031346, A131841.

Programs

Maple

P:=proc(n) local i,k,w,ok,cont; for i from 1 by 1 to n do w:=1; k:=i*2^i-1; ok:=1; 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(120);

Mathematica

Table[wn=n*2^n-1;Length[NestWhileList[Times@@IntegerDigits[#]&, wn, #>=10&]], {n,  105}]-1  (* James C. McMahon, Mar 01 2025 *)

Formula

a(n) = A031346(A003261(n)). - Michel Marcus, Mar 01 2025