OFFSET
1,1
COMMENTS
Conjecture: Any prime number greater than 11 (p) can be the center term of arithmetic progressions prime chain p-6k, p, p+6k, while k>0.
a(n) is also the maximum number k that is needed to find a p(i)-6k, p(i), p(i)+6k kind of arithmetic progressions prime chain for all i <= n, while p(i) is the i-th prime number.
The Mathematica program gives the first 51 items.
LINKS
MATHEMATICA
max = 51; Array[fa, max]; Do[fa[i] = 0, {i, 1, max}]; ct = 0; i = 4; While[ct < max, i++; p = Prime[i]; j = 0; While[j++; df = 6*j; ! ((PrimeQ[p + df]) && (PrimeQ[p - df]))]; If[j <= max, If[fa[j] == 0, fa[j] = i; ct++]]]; Table[fa[i], {i, 1, max}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Lei Zhou, Oct 07 2011
STATUS
approved