A174003 Primes q with q^3 = 2+3*p for a prime p.

2, 5, 11, 17, 41, 47, 89, 101, 107, 239, 311, 347, 431, 479, 521, 641, 701, 719, 761, 839, 881, 941, 947, 1031, 1049, 1301, 1319, 1361, 1499, 1559, 1571, 1667, 1721, 1871, 1931, 2459, 2621, 2687, 2777, 2837, 2861, 2879, 2939, 3347, 3389, 3467, 3539, 3617, 3671, 3917

Offset: 1

Author

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

Keywords

• nonn

Comments

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

A subsequence of A003627.

Examples

			2^3 = 2 + 3 * 2, 2 = prime(1) gives q(1) = 2 = prime(1).
5^3 = 2 + 3 * 41, 41 = prime(13) gives q(2) = 5 = prime(3).
11^3 = 2 + 3 * 443, 443 = prime(86) gives q(3) = 11 = prime(5).
		

References

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000578, A030078, A172271.

Programs

Mathematica

Select[Prime[Range[600]],PrimeQ[(#^3-2)/3]&] (* Harvey P. Dale, Jul 22 2015 *)

Extensions

Typo in a(11) corrected, keyword:base removed - R. J. Mathar, Mar 18 2010