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A233444 Primes that are exactly halfway between the nearest square and the nearest cube.

%I A233444 #9 May 01 2018 21:32:35
%S A233444 2203,90863,185477,388573,613607,912349,1293899,1600919,2146457,
%T A233444 30661333,35608189,81190429,105823093,122753857,204341747,338602837,
%U A233444 368601707,374788121,426958673,498675409,586371239,656232799,665360321,674509487,693132527,1102304669,1180942709
%N A233444 Primes that are exactly halfway between the nearest square and the nearest cube.
%C A233444 A subsequence of A233075.
%H A233444 Robert Israel, <a href="/A233444/b233444.txt">Table of n, a(n) for n = 1..10000</a>
%p A233444 Res:= NULL:
%p A233444 for x from 3 to 2000 do
%p A233444   x3:= x^3;
%p A233444   y:= floor(sqrt(x3));
%p A233444   p:= (x3+y^2)/2;
%p A233444   if p::integer and x3-p <= p - (x-1)^3 and p - y^2 <= (y+1)^2-p and isprime(p) then
%p A233444     Res:= Res, p;
%p A233444   fi;
%p A233444   p:= (x3+(y+1)^2)/2;
%p A233444   if p::integer and p-x3 <= (x+1)^3-p and (y+1)^2-p <= p - y^2 and isprime(p) then
%p A233444       Res:= Res, p;
%p A233444   fi
%p A233444 od:
%p A233444 Res; # _Robert Israel_, May 01 2018
%Y A233444 Cf. A000040, A000290, A000578, A233075.
%Y A233444 Cf. A002760 (Squares and cubes).
%K A233444 nonn
%O A233444 1,1
%A A233444 _Alex Ratushnyak_, Dec 09 2013