A253906 Numbers n such that n^2 + 3 and n^3 + 3 are semiprime.

1, 6, 20, 34, 40, 44, 46, 56, 102, 116, 120, 170, 174, 196, 200, 204, 220, 226, 232, 234, 252, 260, 262, 294, 296, 320, 334, 336, 344, 346, 358, 360, 382, 386, 392, 412, 426, 464, 476, 482, 490, 494, 514, 520, 526, 536, 556, 564, 582, 586, 592, 646, 658, 716

Offset

1,2

Comments

All terms in this sequence, except a(1), are even.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

a(2) = 6;
6^2 + 3 = 39 = 3 * 13;
6^3 + 3 = 219 = 3 * 73;
Both are semiprime.

Mathematica

Select[Range[10^3], k = 3; PrimeOmega[(#^2 + k)] == 2 && PrimeOmega[(#^3 + k)] == 2 &]

Prog

(PARI)
issemiprime(q) = q>0 && bigomega(q)==2
select(n->issemiprime(n^2+3)&&issemiprime(n^3+3), vector(2000, n, n)) \\ Colin Barker, Jan 28 2015

Crossrefs

Cf. A001358, A242331, A108868.

Sequence in context: A140738 A325593 A226363 * A031005 A106528 A031068

Adjacent sequences: A253903 A253904 A253905 * A253907 A253908 A253909

Keyword

nonn

Author

K. D. Bajpai, Jan 24 2015

Status

approved