cp's OEIS Frontend

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.

%I A277118 #18 Dec 23 2024 14:53:44
%S A277118 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,
%T A277118 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,
%U A277118 3,0,3,5,5,3,11,11,5,3,5,7,5,3,0,3,3,3,3,3
%N 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.
%C A277118 Theorem: a(n) takes only the values 0, 3, 5, 7, 9, 11, 13, 15, and 17.
%H A277118 Peter J. C. Moses, <a href="/A277118/b277118.txt">Table of n, a(n) for n = 2..5001</a>
%H A277118 Vladimir Shevelev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2016-September/016801.html">"Nearest" twin primes</a>, Post to seqfan, Sep 21 2016.
%H A277118 Vladimir Shevelev, Peter J. C. Moses, <a href="https://arxiv.org/abs/1610.03385">Constellations of primes generated by twin primes</a>, arXiv:1610.03385 [math.NT], 2016.
%F A277118 a(n) = 3 on a subsequence of measure 1. - _Charles R Greathouse IV_, Oct 17 2016
%o A277118 (PARI) nextcomposite(n)=if(n<4, return(4)); n=ceil(n); if(isprime(n), n+1, n)
%o A277118 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
%o A277118 p=2; forprime(q=3,1e3, if(q-p==2, print1(do(p)", ")); p=q) \\ _Charles R Greathouse IV_, Oct 17 2016
%Y A277118 Cf. A022009, A159559, A229019, A276676, A276703, A276767, A276826, A276831, A276848.
%K A277118 nonn
%O A277118 2,2
%A A277118 _Vladimir Shevelev_ and _Peter J. C. Moses_, Sep 30 2016