cp's OEIS Frontend

A129985 Multiplicative persistence of the prime numbers.

%I A129985 #13 Feb 05 2025 16:18:42
%S A129985 0,0,0,0,1,1,1,1,1,2,1,2,1,2,3,2,3,1,2,1,2,3,2,3,3,1,1,1,1,1,2,1,2,3,
%T A129985 3,1,3,2,2,2,3,1,1,3,3,2,1,2,3,3,2,3,1,2,2,3,2,2,4,2,3,3,1,1,1,2,1,3,
%U A129985 3,2,3,3,3,3,4,3,3,4,1,1,3,1,2,3,2,3,3,2,2,3,4,3,3,3,3,1,1,2,2,2
%N A129985 Multiplicative persistence of the prime numbers.
%H A129985 Alois P. Heinz, <a href="/A129985/b129985.txt">Table of n, a(n) for n = 1..10000</a>
%F A129985 a(n) = A031346(A000040(n)). - _Alois P. Heinz_, Feb 03 2025
%e A129985 229 = prime(50) -> 2*2*9 = 36 -> 3*6 = 18 -> 1*8 = 8 -> persistence(229) = 3 = a(50).
%p A129985 P:=proc(n) local i,k,w,ok,cont,x; for i from 1 by 1 to n do k:=ithprime(i); w:=1; ok:=1; x:=k; 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);
%t A129985 s={};Do[i=0;m=Prime[n];While[m!=Times@@IntegerDigits[m],m=Times@@IntegerDigits[m];i++];AppendTo[s,i],{n,100}];s (* _James C. McMahon_, Feb 03 2025 *)
%Y A129985 Cf. A000040, A031346.
%K A129985 easy,nonn,base
%O A129985 1,10
%A A129985 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 14 2007
%E A129985 Offset corrected by _Alois P. Heinz_, Feb 03 2025