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 A260553 Primes p such that p = q^2 + 2*r^2 where q and r are also primes. 6
 17, 43, 59, 67, 107, 139, 251, 307, 347, 379, 547, 587, 859, 1699, 1867, 1931, 3371, 3499, 3739, 4507, 5059, 5347, 6907, 6971, 7451, 10091, 10627, 10667, 11467, 12491, 18787, 20411, 21227, 22907, 29947, 32059, 32779, 37547, 38651, 39619, 49307, 49747, 53147 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Colin Barker and Chai Wah Wu, Table of n, a(n) for n = 1..1873 n = 1..150 from Colin Barker. EXAMPLE 43 is in the sequence because 43 = 5^2 + 2*3^2 and 43, 5 and 3 are all primes. MATHEMATICA Select[#1^2 + 2 #2^2 & @@ # & /@ Tuples[Prime@ Range@ 60, 2], PrimeQ] // Sort (* Michael De Vlieger, Jul 29 2015 *) PROG (PARI) lista(nn)=forprime(p=2, nn, forprime(r=2, sqrtint(p\2), if (issquare(q2 = p-2*r^2) && isprime(sqrtint(q2)), print1(p, ", ")); ); ); \\ Michel Marcus, Jul 29 2015 (Python) from sympy import prime, isprime n = 5000 A260553_list, plimit = [], prime(n)**2+8 for i in range(1, n): ....q = 2*prime(i)**2 ....for j in range(1, n): ........p = q + prime(j)**2 ........if p < plimit and isprime(p): ............A260553_list.append(p) A260553_list = sorted(A260553_list) # Chai Wah Wu, Jul 30 2015 CROSSREFS Main entry for this sequence is A201613. Cf. A260554, A260555, A260556, A260557. Sequence in context: A118587 A215164 A123592 * A165285 A200321 A165981 Adjacent sequences: A260550 A260551 A260552 * A260554 A260555 A260556 KEYWORD nonn AUTHOR Colin Barker, Jul 29 2015 STATUS approved

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Last modified September 18 13:45 EDT 2024. Contains 376000 sequences. (Running on oeis4.)