A083647 For primes p: Number of steps to reach 2 when iterating f(p) = greatest prime divisor of p-1.

0, 1, 1, 2, 2, 2, 1, 2, 3, 3, 2, 2, 2, 3, 4, 3, 4, 2, 3, 3, 2, 3, 3, 3, 2, 2, 2, 4, 2, 3, 3, 3, 2, 4, 3, 2, 3, 2, 4, 4, 4, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 2, 2, 2, 1, 4, 4, 2, 4, 3, 5, 3, 2, 3, 3, 4, 3, 3, 5, 4, 3, 5, 3, 3, 3, 4, 3, 3, 2, 2, 3, 3, 4, 2, 3, 2, 3, 3, 4, 3, 5, 3, 2, 3, 4, 3, 4, 3, 4, 2, 3, 5, 4, 4, 3

Offset

1,4

Comments

For smallest prime that requires n steps to reach 2 cf. A082449.

Links

Table of n, a(n) for n=1..105.

Example

59 is the 17th prime and takes four steps to reach 2 (59 -> 29 -> 7 ->3 -> 2), so a(17) = 4.

Mathematica

Table[Length[NestWhileList[FactorInteger[#-1][[-1, 1]]&, Prime[n], #!=2&]]-1, {n, 110}] (* Harvey P. Dale, Feb 27 2012 *)

Prog

(PARI) {forprime(p=2, 571, q=p; c=0; while(q>2, fac=factor(q-1); q=fac[matsize(fac)[1], 1]; c++); print1(c, ", "))}

Crossrefs

Cf. A006530, A023503, A082449.

Sequence in context: A162545 A162544 A209323 * A364332 A346389 A056691

Adjacent sequences: A083644 A083645 A083646 * A083648 A083649 A083650

Keyword

nonn

Author

Klaus Brockhaus, May 01 2003

Status

approved