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A276767 Let A_n be the sequence defined in the same way as A159559 but with initial term prime(n), n>=2; a(n) is the smallest m such that for i>=2, A_n(i) - A_2(i) <= A_n(m) - A_2(m).

%I A276767 #9 Sep 17 2016 11:55:15
%S A276767 2,5,17,17,17,359,359,359,163,163,163,163,163,163,163,163,163,448,448,
%T A276767 448,448,448,448,71,71,71,17,17,443,443,443,443,443,443,37,37,2789,
%U A276767 2789,2789,2789,2789,2789,2789,2789,2789,2789,2789,2789,2789,2789,2789,2789
%N A276767 Let A_n be the sequence defined in the same way as A159559 but with initial term prime(n), n>=2; a(n) is the smallest m such that for i>=2, A_n(i) - A_2(i) <= A_n(m) - A_2(m).
%C A276767 By definition, A_2 = A159559.
%e A276767 Let n=4. Set r(i)= A_4(i)- A_2(i), i>=2. Then, by the definition of A_4 and A_2, we have
%e A276767 r(2)=7-3=4,
%e A276767 r(3)=11-5=6, further,
%e A276767 r(4)=...=r(12)=6,
%e A276767 r(13)=r(14)=10,
%e A276767 r(15)=r(16)=11,
%e A276767 r(17)=r(18)=14,
%e A276767 r(19)=...=r(22)=12,
%e A276767 r(23)=...r(26)=10,
%e A276767 r(27)=9,
%e A276767 r(28)=8,
%e A276767 r(29)=...=r(32)=6,
%e A276767 r(33)=...=r(36)=7,
%e A276767 r(37)=r(38)=8,
%e A276767 r(39)=r(40)=7,
%e A276767 r(41)=r(42)=4,
%e A276767 r(43)=r(44)=2,
%e A276767 r(45)=r(46)=1
%e A276767 r(n)=0, n>=47.
%e A276767 So max r(i)=14 and the smallest m such that r(m)=14 is 17.
%e A276767 Thus a(4)=17.
%Y A276767 Cf. A159559, A229019, A276703.
%K A276767 nonn
%O A276767 2,1
%A A276767 _Vladimir Shevelev_, Sep 17 2016
%E A276767 More terms from _Peter J. C. Moses_, Sep 17 2016