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a(n) is the maximal difference between the corresponding terms of sequences defined in the same way as A159559, but with initial terms A001359(n-1)+2 and A001359(n-1) respectively.
4

%I #13 Oct 13 2016 09:42:04

%S 4,14,6,6,6,12,6,8,14,14,18,36,24,65,18,6,10,6,84,14,162,10,54,84,179,

%T 10,23,12,18,18,24,128,18,24,28,10,10,72,34,23,12,18,6,6,12,34,8,644,

%U 12,12,6,29,24,12,18,28,28,24,22,22,10,14,12,12,16,6,58

%N a(n) is the maximal difference between the corresponding terms of sequences defined in the same way as A159559, but with initial terms A001359(n-1)+2 and A001359(n-1) respectively.

%C It seems likely that 6 occurs infinitely often.

%H V. Shevelev, <a href="http://arxiv.org/abs/0904.2101">Several results on sequences which are similar to the positive integers</a>, arXiv:0904.2101 [math.NT], 2009.

%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.

%e Since A276703(3)=4 (cf. example there), a(2)=4.

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

%K nonn

%O 2,1

%A _Vladimir Shevelev_, Sep 19 2016

%E More terms from _Peter J. C. Moses_, Sep 19 2016