%I #8 Jul 31 2023 05:26:22

%S 1,1,3,3,2,1,2,1,4,6,1,1,3,2,5,8,4,3,2,1,4,2,7,3,10,2,1,5,3,3,1,6,2,9,

%T 1,5,3,4,2,3,2,2,5,1,8,9,3,4,2,3,1,12,2,1,10,1,4,2,7,1,8,2,3,1,2,2,3,

%U 11,1,4,9,24,3,5,1,6,18,1,7,1,2,10,1,6,1,2,10,1,8,3,8,3,23,2,4,12,5,17,3,1,6

%N Let f(k) = k + pi(k); a(n) = least number of steps for f(f(f(...(n)))) to reach a prime.

%e a(4) = 3, f(4) = 4+2 = 6, f(6) = 6+3 = 9, f(9)= 9+4 = 13 is prime.

%e a(10) = 4, f(10) = 10+4=14, f(14) = 14+6 = 20, f(20) = 20+8 = 28, f(28) = 28+9 = 37.

%t f[k_] := k + PrimePi[k];

%t a[n_] := NestWhileList[f, f[n], CompositeQ] // Length;

%t Table[a[n], {n, 2, 102}] (* _Jean-François Alcover_, Jul 31 2023 *)

%Y Cf. A090545, A090546.

%K nonn

%O 2,3

%A _Amarnath Murthy_, Dec 09 2003

%E More terms from _Franklin T. Adams-Watters_, Apr 26 2006