A300854 - OEIS

%I #18 Mar 20 2018 00:24:57

%S 3,2,79,5,19,71,211,47,307,181,479,83,1231,293,547,1021,499,683,251,

%T 643,863,2243,1009,1447,2213,3361,4691,2137,2657,2131,929,4621,5851,

%U 1721,7591,1901,11243,3191,19501,3343,2551,2927,997,4703,4177,2789,14537,10331,28723,36899,11311,42433,29429,9631

%N a(n) is the smallest prime p = prime(k) such that A300845(k) = prime(n), or 0 if no such k exists.

%C Is a(n) always positive?

%e a(3) = prime(22) = 79 since least k such that A300845(k) = prime(3) = 5 is 22.

%p f:= proc(p) local q;

%p   q:= 1;

%p   do

%p     q:= nextprime(q);

%p     if isprime(q^2+q*p+p^2) then return q fi;

%p   od

%p end proc:

%p V:= Vector(100):

%p p:= 1: count:= 0:

%p while count < 100 do

%p p:= nextprime(p);

%p v:= numtheory:-pi(f(p));

%p if v <= 100 and V[v] = 0 then V[v]:= p; count:= count+1; fi

%p od:

%p convert(V,list);

%t With[{s = Table[Block[{q = 2}, While[! PrimeQ[q^2 + q p + p^2], q = NextPrime@ q]; q], {p, Prime@ Range[10^4]}]}, TakeWhile[#, # > 0 &] &@ Table[Prime@ First@ FirstPosition[s, p] /. k_ /; ! IntegerQ@ k -> -1, {p, Prime@ Range@ PrimePi@ Max@ s}] ] (* _Michael De Vlieger_, Mar 16 2018 *)

%o (PARI) a300845(n) = {my(p=prime(n)); forprime(q=2, ,if(isprime(p^2+p*q+q^2), return(q)))}

%o a(n) = {my(k=1); while(a300845(k) != prime(n), k++); prime(k); }

%Y Cf. A300845.

%K nonn

%O 1,1

%A _Robert Israel_ and _Altug Alkan_, Mar 13 2018