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A302754 Maximum remainder of prime(p) + prime(q) divided by p + q with p <= q <= n.

%I A302754 #39 Apr 24 2018 06:00:02
%S A302754 0,2,4,6,6,6,6,6,10,18,18,22,22,24,24,24,24,24,24,24,24,26,28,34,44,
%T A302754 46,46,46,46,46,57,58,61,61,61,61,61,61,61,61,61,61,61,61,61,61,61,62,
%U A302754 62,62,62,62,62,70,74,78,82,82,82,82,82,90,110,110,110,110,126,130,136,138,138,142,142,142,142
%N A302754 Maximum remainder of prime(p) + prime(q) divided by p + q with p <= q <= n.
%C A302754 Odd numbers k which are terms of this sequence are 57, 61, 353, 2113, ...
%C A302754 Approximate self-similar growing patterns appear at different scales which suggest a fractal-like structure, see plots in Links section.
%H A302754 Altug Alkan, <a href="/A302754/b302754.txt">Table of n, a(n) for n = 1..10000</a>
%H A302754 Andres Cicuttin, <a href="/A302754/a302754.pdf">Several plots showing similar stair-like patterns</a>
%e A302754 a(1) = 0 because only option is p = q = 1.
%e A302754 a(4) = a(8) = 6 because (prime(4) + prime(4)) mod 8 = (prime(8) + prime(7)) mod 15 = 6 is the largest remainder for both.
%e A302754 a(31) = 57 because (prime(28) + prime(31)) mod 59 = 57 is the largest remainder.
%t A302754 a[n_]:=Table[Table[Mod[Prime[j]+Prime[i],i+j],{i,1,j}],{j,1,n}]//Flatten//Max;
%t A302754 Table[a[n],{n,1,100}]
%o A302754 (PARI) a(n) = vecmax(vector(n, q, vecmax(vector(q, p, (prime(p)+prime(q)) % (p+q)))));
%Y A302754 Cf. A247824, A302245, A302446.
%K A302754 nonn,look
%O A302754 1,2
%A A302754 _Andres Cicuttin_ and _Altug Alkan_, Apr 12 2018