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A090544

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

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, 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, 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

LINKS

Table of n, a(n) for n=2..102.

EXAMPLE

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

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

MATHEMATICA

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

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

Table[a[n], {n, 2, 102}] (* Jean-François Alcover, Jul 31 2023 *)