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