A285706 a(n) = number of iterations x -> A064216(x) needed to reach a nonprime number when starting from prime(n), a(1) = a(2) = 1.

1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 3, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Apr 26 2017

Keywords

• nonn

Comments

Length (or size for the closed cycles: [2] and [3]) of the complete "slipping Cunningham chain of the second kind" starting with prime(n). That is, at the end of every step, the next prime q = 2p-1 "slips" by one step towards smaller primes as A064989(q).

After n = 1, 2 (primes 2 & 3) differs from A181715 for the first time at n=22, where a(22) = 2, while A181715(22) = 3, prime(22) = 79.

Examples

			See examples in A285701.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A064216, A064989, A181715, A246373, A285701.

Cf. A137288 (gives the positions of terms > 1 after its two initial terms).

Programs

Mathematica

Table[If[n <= 2, 1, -1 + Length@ NestWhileList[Apply[Times, FactorInteger[2 # - 1] /. {p_, e_} /; p > 2 :> NextPrime[p, -1]^e] &, Prime@ n, PrimeQ@ # &]], {n, 120}] (* Michael De Vlieger, Apr 26 2017 *)

PARI

A285706(n) = A285701(prime(n)); \\ The rest of code in A285701.

Scheme

(define (A285706 n) (A285701 (A000040 n)))

Formula

a(n) = A285701(A000040(n)).