A227000 Numbers k such that (k+1)^2-k^2 and (k+1)^3-k^3 are both prime.
1, 2, 3, 6, 9, 11, 14, 23, 30, 41, 48, 63, 74, 81, 86, 90, 95, 105, 119, 125, 128, 140, 153, 156, 158, 165, 179, 186, 191, 209, 216, 219, 224, 233, 245, 251, 296, 303, 308, 315, 321, 350, 354, 359, 375, 398, 405, 419, 429, 441, 443, 468, 485, 506, 524, 531, 543, 546, 576
Offset: 1
Keywords
Examples
n=23; n+1=24; 24^2-23^2=47 and 24^3-23^3=1657.
Programs
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Mathematica
Select[Range[576], PrimeQ[(# + 1)^2 - #^2] && PrimeQ[(# + 1)^3 - #^3] &] (* T. D. Noe, Jun 26 2013 *)
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PARI
forprime(p=3,1e3,n=p\2;if(isprime(3*n*(n+1)+1),print1(n", "))) \\ Charles R Greathouse IV, Jun 26 2013