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 A062324 p and p^2 + 4 are both prime. 22
 3, 5, 7, 13, 17, 37, 47, 67, 73, 97, 103, 137, 163, 167, 193, 233, 277, 293, 307, 313, 317, 347, 373, 463, 487, 503, 547, 577, 593, 607, 613, 677, 743, 787, 823, 827, 853, 883, 953, 967, 983, 997, 1087, 1117, 1123, 1237, 1367, 1423, 1447, 1523, 1543, 1613 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Solutions of the equation n' + (n^2+4)' = 2, where n' is the arithmetic derivative of n. [Paolo P. Lava, Nov 09 2012] Equivalent to the definition: largest absolute dimension of Gaussian primes with prime coordinates. As 2 is the only even prime, the only possibility for a Gaussian prime to have prime coordinates is to be of the form +/-2 +/- I*p or +/-p +/-2*I with p^2+4 a prime, i.e., p is a member of this sequence. - Olivier Gérard, Aug 17 2013 When p > 3, p^2 + 2 is never prime. - Zak Seidov, Nov 04 2013 LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 Yang Ji, Several special cases of a square problem, arXiv:2105.05250 [math.GM], 2021. FORMULA a(n) = sqrt(A045637(n) - 4). - Zak Seidov, Nov 04 2013 EXAMPLE a(1) = 3 because 3^2 + 4 = 13 is prime, a(4) = 13 because 13^2 + 4 = 173 is prime. - Zak Seidov, Nov 04 2013 MATHEMATICA Select[Prime/@Range, PrimeQ[ #^2+4]&] PROG (PARI) { n=0; forprime (p=2, 5*10^5, if (isprime(p^2 + 4), write("b062324.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 04 2009 CROSSREFS The corresponding primes p^2+4 are in A045637. Subsequence of A176983. Sequence in context: A003424 A073638 A066464 * A194829 A226794 A300748 Adjacent sequences:  A062321 A062322 A062323 * A062325 A062326 A062327 KEYWORD nonn,easy AUTHOR Reiner Martin (reinermartin(AT)hotmail.com), Jul 12 2001 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Jul 20 2001 Edited by Dean Hickerson, Dec 10 2002 STATUS approved

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Last modified September 27 21:12 EDT 2021. Contains 347698 sequences. (Running on oeis4.)