A145280 Fecundity of n-th prime.

9, 9, 1, 7, 8, 7, 6, 3, 4, 3, 3, 3, 4, 2, 2, 8, 1, 2, 1, 4, 2, 2, 1, 3, 1, 0, 0, 0, 0, 7, 5, 3, 3, 2, 8, 6, 2, 6, 1, 2, 4, 5, 1, 1, 1, 1, 5, 5, 2, 4, 5, 9, 9, 4, 7, 7, 9, 5, 2, 6, 2, 8, 0, 11, 3, 2, 1, 1, 7, 4, 8, 7, 2, 2, 2, 3, 1, 22, 0, 0, 3, 2, 6, 4, 3, 5, 3, 3, 5, 2, 4, 5, 4, 4, 4, 0, 0, 5, 4, 6, 2, 3, 7, 2, 1

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 06 2008

Keywords

• easy
• nonn
• base

Examples

			7 -> 7+7=14 -> 14+1*4=18 -> 18+1*8=26 -> 26+2*6=38 -> 38+3*8=62 -> 62+6*2=74 -> 74+7*4=102 -> 7 steps to reach a zero digit.
		

Crossrefs

Cf. A070562, A145279.

Programs

Maple

P:=proc(i) local a,b,c,ok,k,w,n; for n from 1 by 1 to i do a:=ithprime(n); b:=1; c:=0; ok:=1; while ok=1 do k:=a; w:=1; while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w=0 then ok:=0; else c:=c+1; a:=a+w; fi; od; print(c); od; end: P(100);

Mathematica

f[n_] := Length@ FixedPointList[ # + Times @@ IntegerDigits@# &, n] - 2; Array[f@Prime@# &, 105] (* Robert G. Wilson v, Jun 27 2010 *)

Formula

a(n) = A070562(prime(n)). - Michel Marcus, Aug 01 2015