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A131838
Multiplicative persistence of Woodall numbers.
1
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
1,4
COMMENTS
After the 111th term, all the numbers have some digits equal to zero, thus the persistence is equal to 1.
FORMULA
a(n) = A031346(A003261(n)). - Michel Marcus, Mar 01 2025
EXAMPLE
Woodall number 159 --> 1*5*9=45 --> 4*5=20 --> 2*0=0 thus persistence is 3.
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 *)
CROSSREFS
KEYWORD
easy,nonn,base,changed
AUTHOR
STATUS
approved