A276831 - OEIS

%I #21 Oct 18 2016 14:20:57

%S 5,17,11,5,3,17,3,11,11,5,31,107,13,333,17,5,3,3,281,5,997,3,487,659,

%T 5178,5,15,3,23,53,13,1567,13,13,181,3,5,443,37,21,19,11,5,3,5,5,7,

%U 20786,13,7,5,21,3,5,17,61,31,23,7,3,11,5,11,5,3,3,157,37

%N For a lesser p=A001359(n-1), n>=2, of twin primes, let B_k be the sequence defined as A159559 but with initial term k; a(n) is the smallest m such that B_(p+2)(m)-B_p(m) = max_{t>=2} (B_(p+2)(t)-B_p(t)).

%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.

%F B_(p+2)(a(n)) - B_p(a(n)) = A276826(n).

%e Let n=2, p=A001359(1)=3. Then B_3(2)=3, B_3(3)=5, B_3(4)=6, B_3(5)=7, B_3(6)=8, B_3(7)=11, B_3(8)=12, B_3(9)=14, B_3(10)=15, B_3(11)=17;

%e Further, B_5(2)=5, B_5(3)=7, B_5(4)=8, B_5(5)=11, B_5(6)=12, B_5(7)=13, B_5(8)=14, B_5(9)=15, B_5(10)=16, B_5(11)=17 and, beginning with t=11,

%e B_3 merges with B_5. So, max(B_5(t)-B_3(t))=4 reaching at t=5 and t=6.

%e Thus a(2)=min(5,6)=5.

%Y Cf. A001359, A159559, A229019, A276676, A276703, A276767, A276826.

%K nonn

%O 2,1

%A _Vladimir Shevelev_, Sep 20 2016

%E More terms from _Peter J. C. Moses_, Sep 20 2016