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A284412 a(1) = 1, a(2) = 2; a(n) is the largest prime <= (a(a(n-1)) + a(n-a(n-1))) for n > 2.

%I A284412 #14 Mar 30 2017 01:14:48
%S A284412 1,2,3,3,5,5,7,7,7,7,7,11,7,13,7,13,7,13,11,13,13,13,13,13,17,13,19,
%T A284412 17,17,13,19,17,19,17,19,17,19,19,23,19,23,23,23,23,23,23,23,29,29,29,
%U A284412 29,29,29,31,31,31,31,37,31,31,31,37,31,37,31,37,31,37,31,41,31,41,37,37,37,41,37,41,41,43
%N A284412 a(1) = 1, a(2) = 2; a(n) is the largest prime <= (a(a(n-1)) + a(n-a(n-1))) for n > 2.
%H A284412 Altug Alkan, <a href="/A284412/b284412.txt">Table of n, a(n) for n = 1..10000</a>
%H A284412 Altug Alkan, <a href="/A284412/a284412.png">Scatterplot of n-2*a(n)</a>
%H A284412 Altug Alkan, <a href="/A284412/a284412_2.png">Plot of a(n)/n</a>
%F A284412 a(1) = 1, a(2) = 2; a(n) = A007917(a(a(n-1)) + a(n-a(n-1))) for n > 2.
%e A284412 a(6) = 5 because a(a(5)) + a(6 - a(5)) = a(5) + a(1) = 5 + 1 = 6 and A007917(6) = 5
%o A284412 (PARI) a=vector(1000); a[1]=1; a[2]=2; for(n=3, #a, a[n] = precprime(a[a[n-1]]+a[n-a[n-1]])); a
%Y A284412 Cf. A004001, A007917, A284374, A284383, A284397.
%K A284412 nonn
%O A284412 1,2
%A A284412 _Altug Alkan_, Mar 26 2017