A131837 Multiplicative persistence of Cullen numbers.
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, 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, 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
Offset: 1
Examples
Cullen number 65 --> 6*5=30 --> 3*0=0 thus persistence is 2.
Programs
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Maple
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);
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Mathematica
Table[cn=n*2^n+1;Length[NestWhileList[Times@@IntegerDigits[#]&, cn, #>=10&]], {n, 0, 104}]-1 (* James C. McMahon, Mar 01 2025 *)
Comments