A284397 - OEIS

%I #18 Mar 30 2017 01:14:42

%S 1,2,3,3,3,5,5,5,5,5,5,7,7,7,7,7,7,7,7,11,11,7,7,11,11,11,11,11,11,11,

%T 11,13,17,17,13,13,13,17,17,13,13,17,17,17,17,17,17,17,17,19,23,19,17,

%U 23,19,19,19,23,23,19,19,23,23,19,19,23,23,23,23,23,23,23,23,23

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

%H Altug Alkan, <a href="/A284397/b284397.txt">Table of n, a(n) for n = 1..10000</a>

%H Altug Alkan, <a href="/A284397/a284397.png">Alternative scatterplot of A284397</a>

%H Altug Alkan, <a href="/A284397/a284397_1.png">Scatterplot of 4*a(n)-n</a>

%F a(1) = 1, a(2) = 2; a(n) = A007917(a(a(n-1)) + a(n-a(n-2)-1)) for n > 2.

%e a(6) = 5 because a(a(5)) + a(6 - a(4) - 1) = a(3) + a(2) = 3 + 2 = 5 and A007917(5) = 5.

%t a[n_]:= If[n<3, n, Prime@ PrimePi[a[a[n - 1]] + a[n - a[n - 2] - 1]]]; Table[a[n],{n, 1, 50}] (* _Indranil Ghosh_, Mar 26 2017 *)

%o (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-2]-1])); a

%Y Cf. A005185, A007917, A055748, A284374, A284383.

%K nonn

%O 1,2

%A _Altug Alkan_, Mar 26 2017