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A083647 For primes p: Number of steps to reach 2 when iterating f(p) = greatest prime divisor of p-1. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A056691 A262982 A205011

Adjacent sequences:  A083644 A083645 A083646 * A083648 A083649 A083650

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, May 01 2003

STATUS

approved

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Last modified August 24 22:49 EDT 2019. Contains 326314 sequences. (Running on oeis4.)