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

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

Offset: 1

Author

Lei Zhou, Oct 07 2011

Keywords

• nonn

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.

Examples

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

Links

• Definition of Arithmetic Progressions of Primes

Crossrefs

Cf. A078498, A078497, A001748.

Programs

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}]