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Positive numbers k such that k^3 +- (k-1)^2 are primes.
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%I #11 Sep 08 2022 08:45:32

%S 3,6,7,13,21,73,75,90,91,97,106,115,157,201,208,238,291,300,315,358,

%T 385,405,420,460,505,523,540,651,658,798,810,825,927,942,1000,1105,

%U 1125,1135,1186,1197,1278,1315,1365,1378,1380,1410,1417,1476,1480,1483,1557

%N Positive numbers k such that k^3 +- (k-1)^2 are primes.

%e 3^3 +- 2^2 -> (23, 31) (both primes);

%e 7^3 +- 6^2 -> (307, 379) (both primes).

%t Select[Range[900],PrimeQ[ #^3-(#-1)^2]&&PrimeQ[ #^3+(#-1)^2]&]

%o (Magma) [n: n in [0..500] | IsPrime(n^3-(n-1)^2)and IsPrime(n^3 +(n-1)^2)] // _Vincenzo Librandi_, Nov 24 2010

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 21 2008

%E More terms from _Vincenzo Librandi_, Mar 26 2010