A277118 For a lesser p of twin primes, let B_k be A159559, but with initial term k; then a(n) is the smallest m such that B_(p+2)(m)-B_p(m)>6, where p = A001359(n-1), or a(n) = 0 if there is no such m.

0, 13, 0, 0, 0, 9, 0, 11, 11, 5, 3, 15, 3, 7, 3, 0, 3, 0, 3, 5, 7, 3, 11, 5, 3, 5, 11, 3, 9, 3, 3, 7, 3, 5, 5, 3, 5, 3, 5, 11, 3, 5, 0, 0, 5, 5, 7, 5, 13, 7, 0, 5, 3, 3, 3, 3, 7, 3, 3, 3, 5, 3, 7, 3, 3, 0, 3, 5, 5, 3, 11, 11, 5, 3, 5, 7, 5, 3, 0, 3, 3, 3, 3, 3

Offset

2,2

Comments

Theorem: a(n) takes only the values 0, 3, 5, 7, 9, 11, 13, 15, and 17.

Links

Peter J. C. Moses, Table of n, a(n) for n = 2..5001

Vladimir Shevelev, "Nearest" twin primes, Post to seqfan, Sep 21 2016.

Vladimir Shevelev, Peter J. C. Moses, Constellations of primes generated by twin primes, arXiv:1610.03385 [math.NT], 2016.

Formula

a(n) = 3 on a subsequence of measure 1. - Charles R Greathouse IV, Oct 17 2016

Prog

(PARI) nextcomposite(n)=if(n<4, return(4)); n=ceil(n); if(isprime(n), n+1, n)
do(p)=my(a=p, b=p+2, f); for(n=3, 17, f=if(isprime(n), nextprime, nextcomposite); a=f(a+1); b=f(b+1); if(b-a > 6, return(n))); 0
p=2; forprime(q=3, 1e3, if(q-p==2, print1(do(p)", ")); p=q) \\ Charles R Greathouse IV, Oct 17 2016

Crossrefs

Cf. A022009, A159559, A229019, A276676, A276703, A276767, A276826, A276831, A276848.

Sequence in context: A081357 A127708 A094896 * A200065 A067155 A277255

Adjacent sequences: A277115 A277116 A277117 * A277119 A277120 A277121

Keyword

nonn

Author

Vladimir Shevelev and Peter J. C. Moses, Sep 30 2016

Status

approved