A108868 -id:A108868 - cp's OEIS frontend

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

K. D. Bajpai, Jan 24 2015

nonn

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

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

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

Cf. A001358, A242331, A108868.

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

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

A253907 Numbers n such that n^2 + 3, n^3 + 3, n^4 + 3, n^5 + 3, n^6 + 3 and n^7 + 3 are semiprime.

Original entry on oeis.org

1, 976, 5380, 16582, 17864, 22316, 27922, 34930, 44954, 50744, 61264, 72670, 107534, 147776, 193774, 195266, 240170, 260920, 265292, 281582, 314462, 337832, 342014, 367060, 379784, 383930, 384704, 392050, 421226, 455734, 463790, 498134, 499306, 510194, 538384

Offset: 1

K. D. Bajpai, Jan 24 2015

nonn

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

Subsequence of A253906.

			a(2) = 976;
976^2 + 3 = 952579 = 43 * 22153;
976^3 + 3 = 929714179 = 1013 * 917783;
976^4 + 3 = 907401035779 = 7 * 129628719397;
976^5 + 3 = 885623410917379 = 2224441 * 398133019;
976^6 + 3 = 864368449055358979 = 97327 * 8881075642477;
976^7 + 3 = 843623606278030360579 = 16403765263 * 51428656333;
All six are semiprime.

K. D. Bajpai, Table of n, a(n) for n = 1..555

Cf. A001358, A108868, A242331, A253906.

Select[Range[10^5], k = 3; PrimeOmega[(#^2 + k)] == 2 && PrimeOmega[(#^3 + k)] == 2 && PrimeOmega[(#^4 + k)] == 2 && PrimeOmega[(#^5 + k)] == 2 &&  PrimeOmega[(#^6 + k)] == 2  && PrimeOmega[(#^7 + k)] == 2 &]
Select[Range[54*10^4],Union[PrimeOmega[#^Range[2,7]+3]]=={2}&] (* Harvey P. Dale, Jul 30 2022 *)

cp's OEIS Frontend

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

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