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.

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

1,2

Comments

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

Subsequence of A253906.

Links

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

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A001358, A108868, A242331, A253906.

Sequence in context: A251845 A254072 A253363 * A233984 A205252 A190400

Adjacent sequences: A253904 A253905 A253906 * A253908 A253909 A253910

Keyword

nonn

Author

K. D. Bajpai, Jan 24 2015

Status

approved