A181696 Number of iterations p -> ap+b needed to get a composite number, starting with p=prime(n) and the least even a>0 and odd b<a, b>0 such that a*prime(n)+b is prime.

5, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 6, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 5, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 4, 3, 2, 2

Offset

1,1

Comments

The length of the prime chain starting at prime(n), with the least parameters a (>0, even) and b (>0, <a and odd) such that this chain is at least of length 2.

Links

Table of n, a(n) for n=1..168.

D. Broadhurst, Warren D. Smith, et al., Prime chains x -> Ax+B. Yahoo group "primenumbers", Nov 2010.

David Broadhurst and others, Prime chains x-->Ax+B, digest of 143 messages in primenumbers Yahoo group, Nov 12, 2010 - Jan 7, 2011.

David Broadhurst and others, Prime chains x-->Ax+B, digest of 143 messages in primenumbers Yahoo group, Nov 12, 2010 - Jan 7, 2011. [Cached copy]

Prog

(PARI) chainlen(n)={ n=prime(n); forstep(a=2, 1e9, 2, forstep(b=1, a, 2, ispseudoprime(a*n+b)|next; for(c=1, 1e9, ispseudoprime(n=a*n+b) | return(c)))) }

Crossrefs

Sequence in context: A181697 A317175 A257480 * A157121 A368690 A083241

Adjacent sequences: A181693 A181694 A181695 * A181697 A181698 A181699

Keyword

nonn

Author

M. F. Hasler, Nov 16 2010

Status

approved