cp's OEIS Frontend

A196934 a(n) is the first occurrence of n in sequence A078498.

%I A196934 #11 Apr 03 2023 10:36:12
%S A196934 5,8,18,14,25,38,43,50,61,48,132,167,100,88,151,217,176,216,270,214,
%T A196934 300,785,429,687,308,1083,374,644,713,320,840,608,654,577,1005,1409,
%U A196934 1631,1215,928,1386,2304,1984,1203,2336,853,1638,1899,1806,1974,1594,1228
%N A196934 a(n) is the first occurrence of n in sequence A078498.
%C A196934 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.
%C A196934 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.
%C A196934 The Mathematica program gives the first 51 items.
%H A196934 Definition of <a href="https://t5k.org/top20/page.php?id=14">Arithmetic Progressions of Primes</a>
%e A196934 A078498(5)=1 (take the offset 5),  so a(1)=5;
%e A196934 2 first occurs as A078498(8), so a(2)=8;
%t A196934 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}]
%Y A196934 Cf. A078498, A078497, A001748.
%K A196934 nonn
%O A196934 1,1
%A A196934 _Lei Zhou_, Oct 07 2011