

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
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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[300], 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



