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Primes q with q^3 = 2+3*p for a prime p.
1

%I #4 Jul 22 2015 15:43:23

%S 2,5,11,17,41,47,89,101,107,239,311,347,431,479,521,641,701,719,761,

%T 839,881,941,947,1031,1049,1301,1319,1361,1499,1559,1571,1667,1721,

%U 1871,1931,2459,2621,2687,2777,2837,2861,2879,2939,3347,3389,3467,3539,3617,3671,3917

%N Primes q with q^3 = 2+3*p for a prime p.

%C q^3 = prime(1) + prime(2) * p.

%C A subsequence of A003627.

%D Wolfgang M. Schmidt, Diophantine approximations and Diophantine equations. Lecture Notes in Mathematics, Springer-Verlag, 2000

%H Harvey P. Dale, <a href="/A174003/b174003.txt">Table of n, a(n) for n = 1..1000</a>

%e 2^3 = 2 + 3 * 2, 2 = prime(1) gives q(1) = 2 = prime(1).

%e 5^3 = 2 + 3 * 41, 41 = prime(13) gives q(2) = 5 = prime(3).

%e 11^3 = 2 + 3 * 443, 443 = prime(86) gives q(3) = 11 = prime(5).

%t Select[Prime[Range[600]],PrimeQ[(#^3-2)/3]&] (* _Harvey P. Dale_, Jul 22 2015 *)

%Y Cf. A000578, A030078, A172271.

%K nonn

%O 1,1

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 05 2010

%E Typo in a(11) corrected, keyword:base removed - _R. J. Mathar_, Mar 18 2010