A277118 - OEIS

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A277118

For a lesser p of twin primes, let B_k beA159559,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.

4

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

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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 ShevelevandPeter J. C. Moses,Sep 30 2016

STATUS

approved