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

1,1

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

Table of n, a(n) for n=1..51.

Definition of Arithmetic Progressions of Primes

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

Cf. A078498, A078497, A001748.

Sequence in context: A192170 A280251 A104321 * A359949 A291752 A237276

Adjacent sequences: A196931 A196932 A196933 * A196935 A196936 A196937

Keyword

nonn

Author

Lei Zhou, Oct 07 2011

Status

approved