A080189 a(n) = k such that f^k(prime(n)) = 2, where f is the mapping of primes > 2 to primes defined by A052248.

0, 1, 2, 3, 2, 4, 2, 3, 5, 3, 3, 4, 4, 6, 3, 4, 3, 4, 6, 2, 5, 5, 7, 4, 3, 3, 5, 2, 5, 5, 7, 7, 6, 6, 3, 4, 6, 8, 7, 5, 3, 5, 2, 4, 3, 6, 6, 6, 4, 4, 6, 3, 8, 8, 8, 5, 3, 7, 7, 4, 4, 5, 6, 5, 7, 9, 8, 6, 4, 5, 4, 6, 5, 4, 3, 5, 4, 7, 4, 7, 4, 7, 2, 6, 3, 7, 5, 5, 3, 7, 4, 9, 9, 8, 9, 8, 9, 4, 4, 8, 8, 5, 5, 4, 3

Offset

1,3

Comments

Since the largest of all prime factors of the numbers between prime p and the next prime is smaller than p, we have p > f(p) > f^2(p) > ... > 2, so a(n) is finite for all n.

Links

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

Example

prime(6) = 13, f(13) = 7, f(7) = 5, f(5) = 3, f(3) = 2, so f^4(13) = 2 and a(6) = 4.

Prog

(PARI) {forprime(k=2, 580, c=0; p=k; while(p>2, q=nextprime(p+1); m=0; for(j=p+1, q-1, f=factor(j); a=f[matsize(f)[1], 1]; if(m<a, m=a)); p=m; c++); print1(c, ", "))}

Crossrefs

Cf. A052248.

Sequence in context: A368710 A080771 A025477 * A076399 A360729 A370328

Adjacent sequences: A080186 A080187 A080188 * A080190 A080191 A080192

Keyword

nonn

Author

Klaus Brockhaus, Feb 10 2003

Status

approved