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

1,8

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

29 -> 2 + 9 = 11 -> 1 + 1 = 2 -> persistence = 2
487 -> 4 + 8 + 7 = 19 -> 1 + 9 = 10 -> 1 + 0 = 1 -> persistence = 3

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 *)

Crossrefs

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

Sequence in context: A188512 A081129 A022934 * A341765 A104248 A358359

Adjacent sequences: A107447 A107448 A107449 * A107451 A107452 A107453

Keyword

base,easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 22 2007

Status

approved