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%I #4 Feb 24 2023 15:54:44
%S 4,9,81,144,900,3249,4356,7569,12321,14400,38025,59049,60516,77841,
%T 142884,145161,186624,202500,221841,230400,356409,423801,576081,
%U 656100,870489,974169,1108809,1838736,1855044,1971216,1979649,1988100,2396304
%N Squares s(n) such that cube(n)-square(n)-1 and cube(n)+square(n)+1 are primes.
%C 2^3-2^2-1=3;2^3+2^2+1=13, 3^3-3^2-1=17;3^3+3^2+1=37, ...
%t lst={};Do[c=n^3;s=n^2;p1=c-s-1;p2=c+s+1;If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,s]],{n,7!}];lst
%t #^2&/@Select[Range[1600],AllTrue[#^3+{-#^2-1,#^2+1},PrimeQ]&] (* _Harvey P. Dale_, Feb 24 2023 *)
%Y Cf. A155929, A155930
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 30 2009
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