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%I #27 Jan 02 2023 12:30:52
%S 3,11,17,29,59,227,269,1277,1289,1607,2129,2789,3527,3917,4637,4787,
%T 5639,8999,13679,14549,18119,27737,36779,38447,39227,44267,62129,
%U 71327,75989,80669,83219,88799,93479,97367,99707,113147,113159,115769,122027,122387,124337,124769,132749,150209,160079
%N For a lesser p of twin primes, let B_(p+2) and B_p be sequences defined as A159559, but with initial terms p+2 and p respectively. The sequence lists p for which all differences B_(p+2)(n)-B_p(n)<=6.
%C B_(p+2)(n) - B_p(n) < 6 for all n >= 2 if and only if p = 3.
%C It is astonishing that, although terms a(n) == 7 or 9 (mod 10) occur often, the first terms a(n)==1 (mod 10) are 11, 165701, ... (cf. A022009). This phenomenon is explained in the Shevelev link.
%H Charles R Greathouse IV, <a href="/A276848/b276848.txt">Table of n, a(n) for n = 1..10000</a>
%H Vladimir Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2016-September/016801.html">"nearest" twin primes</a>, Post to seqfan, Sep 21 2016.
%H 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.
%o (PARI) nextcomposite(n)=if(n<4, return(4)); n=ceil(n); if(isprime(n), n+1, n)
%o is(n)=if(!isprime(n) || !isprime(n+2), return(0)); my(p=n,q=n+2,k=2,f); while(p!=q && q-p<7, f=if(isprime(k++),nextprime,nextcomposite); p=f(p+1); q=f(q+1)); p==q \\ _Charles R Greathouse IV_, Sep 21 2016
%Y Cf. A001359, A159559, A229019, A276676, A276703, A276767, A276826, A276831, A022009.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Sep 21 2016
%E More terms from _Peter J. C. Moses_, Sep 21 2016
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