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A131837
Multiplicative persistence of Cullen numbers.
1
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
1,4
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(A002064(n)). - Michel Marcus, Mar 01 2025
EXAMPLE
Cullen number 65 --> 6*5=30 --> 3*0=0 thus persistence is 2.
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);
MATHEMATICA
Table[cn=n*2^n+1; Length[NestWhileList[Times@@IntegerDigits[#]&, cn, #>=10&]], {n, 0, 104}]-1 (* James C. McMahon, Mar 01 2025 *)
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
STATUS
approved