A107450 Additive persistence of the prime numbers.
0, 0, 0, 0, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 1, 2, 2
Offset: 1
Examples
29 -> 2 + 9 = 11 -> 1 + 1 = 2 -> persistence = 2 487 -> 4 + 8 + 7 = 19 -> 1 + 9 = 10 -> 1 + 0 = 1 -> persistence = 3
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Programs
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Maple
P:=proc(n) local i,k,w,ok,cont; for i from 1 by 1 to n do k:=ithprime(i); w:=0; 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(100);
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Mathematica
Table[Length[NestWhileList[Total[IntegerDigits[#]]&,n,#>9&]]-1,{n, Prime[ Range[100]]}] (* Harvey P. Dale, Aug 05 2014 *)