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 A153477 Primes p such that 2p+1 and 2p^2+4p+1 are also prime. 1
 2, 3, 5, 23, 41, 131, 191, 293, 443, 653, 719, 1031, 1409, 1451, 1973, 2063, 2273, 2753, 3023, 3593, 3911, 4349, 4391, 4793, 5003, 5039, 5081, 5171, 5231, 5333, 5501, 6053, 6113, 7433, 7541, 7643, 8273, 8741, 8969, 9371, 10691, 10709, 11321, 11909, 12119 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A005384. If p = 3*2(m-1)-1, q = 2*p+1 and r=2*p^2+4*p+1 (m>1), then p*q*2^m and r*2^m are amicable numbers (A063990), this follows immediately from Thabit ibn Kurrah theorem. - Vincenzo Librandi, Sep 30 2013 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Thâbit ibn Kurrah Rule. EXAMPLE For prime p = 5, 2p+1 = 11 is prime and 2p^2+4p+1 = 71 is prime; for p=293, 2p+1 = 587 is prime and 2p^2+4p+1 = 172871 is prime. For p=5=3*2-1, q=11, r=71, we have 5*11*4=220 and 71*4=284, which are amicable numbers. - Vincenzo Librandi, Sep 30 2013 MAPLE a := proc (n) if isprime(n) = true and isprime(2*n+1) = true and isprime(2*n^2+4*n+1) = true then n else end if end proc: seq(a(n), n = 1 .. 13000); # Emeric Deutsch, Jan 02 2009 MATHEMATICA Select[Prime[Range[1500]], And@@PrimeQ[{2#+1, 2#^2+4#+1}]&] (* Harvey P. Dale, Sep 23 2012 *) PROG (Magma) [p: p in PrimesUpTo(12200) | IsPrime(2*p+1) and IsPrime(2*p^2+4*p+1) ]; CROSSREFS Cf. A005384 (Sophie Germain primes p: 2p+1 is also prime). Sequence in context: A215317 A104736 A090710 * A080016 A171432 A214703 Adjacent sequences: A153474 A153475 A153476 * A153478 A153479 A153480 KEYWORD nonn AUTHOR Vincenzo Librandi, Dec 27 2008 EXTENSIONS Edited, corrected (2 added) and extended beyond a(8) by Klaus Brockhaus, Jan 01 2009 Extended by Emeric Deutsch, Jan 02 2009 STATUS approved

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Last modified November 27 22:56 EST 2022. Contains 358406 sequences. (Running on oeis4.)