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 A266966 Primes of the form x^2 + y^2 where x^2 + x*y + y^2 is also prime with positive x and y. 0
 2, 5, 13, 37, 41, 53, 73, 109, 137, 157, 173, 181, 193, 197, 233, 349, 373, 401, 421, 457, 509, 541, 557, 569, 577, 613, 661, 709, 733, 757, 769, 821, 877, 941, 1009, 1033, 1069, 1117, 1129, 1193, 1201, 1237, 1301, 1373, 1453, 1493, 1549, 1597, 1621, 1657, 1669, 1697, 1721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence focuses on the positive values of x and y. Otherwise, for example 17 = 4^2 + (-1)^2 and 4^2 + 4*(-1) + (-1)^2 = 13 is prime too. Corresponding generalized cuban primes are 3, 7, 19, 43, 61, 67, 97, 139, 181, 199, 211, 223, 271, 277, 337, 421, 439, 499, 541, 601, 619, 631, 751, 787, 811, 823, 829, 919, ... LINKS EXAMPLE 5 is a term because 2^2 + 1^2 = 5 is prime and 2^2 + 2*1 + 1^2 = 7 is prime. 13 is a term because 3^2 + 2^2 = 13 is prime and 3^2 + 3*2 + 2^2 = 19 is prime. 37 is a term because 6^2 + 1^2 = 37 is prime and 6^2 + 6*1 + 1^2 = 43 is prime. MATHEMATICA lim = 50; Take[Select[Union@ Flatten@ Table[ If[PrimeQ[Abs[x^2 + x y + y^2]], x^2 + y^2, Nothing], {x, lim}, {y, lim}], PrimeQ], 53] (* Michael De Vlieger, Jan 07 2016 *) PROG (PARI) list(lim) = my(v=List(), t); lim\=1; for(x=1, sqrtint(lim), for(y=1, min(sqrtint(lim-x^2), x), if(isprime(t=x^2+y^2) && isprime(x^2+x*y+y^2), listput(v, t)))); vecsort(Vec(v), , 8) CROSSREFS Cf. A002313, A007645. Sequence in context: A148299 A148300 A038982 * A019415 A262203 A175118 Adjacent sequences:  A266963 A266964 A266965 * A266967 A266968 A266969 KEYWORD nonn AUTHOR Altug Alkan, Jan 07 2016 STATUS approved

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Last modified May 19 17:07 EDT 2022. Contains 353847 sequences. (Running on oeis4.)