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 A237360 Numbers n of the form p^2+p+1 (for prime p) such that n^2+n+1 is also prime. 3
 57, 381, 993, 4557, 16257, 32943, 49953, 58323, 109893, 135057, 167691, 214833, 237657, 453603, 503391, 564753, 658533, 678153, 780573, 995007, 1248807, 1516593, 1746363, 2218611, 2400951, 3465183, 3738423, 4340973, 4750221, 5232657, 6118203 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..10000 EXAMPLE 57 = 7^2+7+1 (7 is prime) and 57^2+57+1 = 3307 is also prime. Thus, 57 is a member of this sequence. MAPLE for k from 1 do     p := ithprime(k) ;     n := numtheory[cyclotomic](3, p) ;     pn := numtheory[cyclotomic](3, n) ;     if isprime( pn) then         print(n) ;     end if; end do: # R. J. Mathar, Feb 07 2014 MATHEMATICA Select[Table[p^2+p+1, {p, Prime[Range[500]]}], PrimeQ[#^2+#+1]&] (* Harvey P. Dale, Feb 09 2014 *) PROG (Python) import sympy from sympy import isprime {print(n**2+n+1) for n in range(10**4) if isprime(n) and isprime((n**2+n+1)**2+(n**2+n+1)+1)} (PARI) s=[]; forprime(p=2, 4000, if(isprime(p^4+2*p^3+4*p^2+3*p+3), s=concat(s, p^2+p+1))); s \\ Colin Barker, Feb 07 2014 CROSSREFS Cf. A060800, A002383. Sequence in context: A209517 A097200 A211147 * A076459 A268260 A184224 Adjacent sequences:  A237357 A237358 A237359 * A237361 A237362 A237363 KEYWORD nonn AUTHOR Derek Orr, Feb 06 2014 STATUS approved

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Last modified June 20 17:27 EDT 2019. Contains 324234 sequences. (Running on oeis4.)