

A196935


a(n) is the number of arithmetic progressions prime chains in the form of p(n)6k, p(n), p(n)+6k, while k > 0 and p(n) > 6k.


1



1, 1, 2, 1, 2, 3, 1, 3, 3, 3, 4, 4, 5, 3, 4, 6, 5, 4, 4, 6, 5, 7, 6, 6, 6, 5, 7, 8, 9, 6, 10, 8, 7, 6, 9, 8, 9, 6, 8, 10, 10, 6, 9, 10, 11, 8, 11, 10, 9, 13, 13, 13, 13, 9, 10, 13, 11, 12, 14, 15, 11, 12, 12, 14, 17, 13, 18, 14, 14, 16, 14, 16, 14, 16, 15, 16
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OFFSET

5,3


COMMENTS

Conjecture: a(n) > 0 for all n >= 5.
The Mathematica program gives term 5 through 80.


LINKS

Table of n, a(n) for n=5..80.
Definition of Arithmetic Progressions of Primes


EXAMPLE

n = 5, p(5) = 11; {5, 11, 17} forms a difference 6 Arithmetic Progressions Prime chain. And this is the only occurrence for 11. So a(5) = 1;
n = 6, p(6) = 13; {7, 13, 19} forms a difference 6 Arithmetic Progressions Prime chain. And this is the only occurrence for 11. So a(6) = 1;
...
n = 10, p(10) = 29; {17, 29, 41}, {11, 29, 47}, {5, 29, 53} form Arithmetic Progressions Prime chains with difference 12, 18, 24 respectively. So a(10) = 3;


MATHEMATICA

Table[ct = 0; p = Prime[i]; j = 0; While[j++; df = 6*j; df < p, If[(PrimeQ[p + df]) && (PrimeQ[p  df]), ct++]]; ct, {i, 5, 80}]


CROSSREFS

Cf. A196934, A078498, A078497, A001748.
Sequence in context: A326921 A286343 A075106 * A226314 A036995 A225597
Adjacent sequences: A196932 A196933 A196934 * A196936 A196937 A196938


KEYWORD

nonn,easy


AUTHOR

Lei Zhou, Oct 07 2011


STATUS

approved



