

A196934


a(n) is the first occurrence of n in sequence A078498.


2



5, 8, 18, 14, 25, 38, 43, 50, 61, 48, 132, 167, 100, 88, 151, 217, 176, 216, 270, 214, 300, 785, 429, 687, 308, 1083, 374, 644, 713, 320, 840, 608, 654, 577, 1005, 1409, 1631, 1215, 928, 1386, 2304, 1984, 1203, 2336, 853, 1638, 1899, 1806, 1974, 1594, 1228
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OFFSET

1,1


COMMENTS

Conjecture: Any prime number greater than 11 (p) can be the center term of arithmetic progressions prime chain p6k, 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 ith prime number.
The Mathematica program gives the first 51 items.


LINKS



EXAMPLE

A078498(5)=1 (take the offset 5), so a(1)=5;
2 first occurs as A078498(8), so a(2)=8;


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



STATUS

approved



