This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A131837 #16 Mar 01 2025 11:17:02
%S A131837 0,0,0,2,2,1,2,2,1,1,1,2,2,1,3,2,1,2,2,2,1,1,3,2,1,1,1,2,2,2,2,1,2,2,
%T A131837 2,1,1,1,1,1,1,1,2,2,1,2,2,1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,
%U A131837 1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A131837 Multiplicative persistence of Cullen numbers.
%C A131837 After the 111th term, all the numbers have some digits equal to zero, thus the persistence is equal to 1.
%F A131837 a(n) = A031346(A002064(n)). - _Michel Marcus_, Mar 01 2025
%e A131837 Cullen number 65 --> 6*5=30 --> 3*0=0 thus persistence is 2.
%p A131837 P:=proc(n) local i,k,w,ok,cont; for i from 0 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);
%t A131837 Table[cn=n*2^n+1;Length[NestWhileList[Times@@IntegerDigits[#]&, cn, #>=10&]], {n, 0, 104}]-1 (* _James C. McMahon_, Mar 01 2025 *)
%Y A131837 Cf. A002064, A031346, A131840.
%K A131837 easy,nonn,base
%O A131837 1,4
%A A131837 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jul 20 2007