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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.
1
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
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 A372286 A368690
KEYWORD
nonn
AUTHOR
M. F. Hasler, Nov 16 2010
STATUS
approved