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

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 *)

Crossrefs

Cf. A090545, A090546.

Sequence in context: A286443 A075522 A186144 * A283755 A038766 A080993

Adjacent sequences: A090541 A090542 A090543 * A090545 A090546 A090547

Keyword

nonn

Author

Amarnath Murthy, Dec 09 2003

Extensions

More terms from Franklin T. Adams-Watters, Apr 26 2006

Status

approved