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A253906 Numbers n such that n^2 + 3 and n^3 + 3 are semiprime. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 22 09:50 EDT 2022. Contains 353949 sequences. (Running on oeis4.)