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

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 22 2007

Keywords

• base
• easy
• nonn

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

Crossrefs

Cf. A031286 (additive persistence), A129985 (multiplicative persistence of primes).

Programs

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);

Mathematica

Table[Length[NestWhileList[Total[IntegerDigits[#]]&,n,#>9&]]-1,{n, Prime[ Range[100]]}] (* Harvey P. Dale, Aug 05 2014 *)