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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
All terms in this sequence, except a(1), are even.
Subsequence of A253906.
LINKS
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
Sequence in context: A251845 A254072 A253363 * A233984 A205252 A190400
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Jan 24 2015
STATUS
approved

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Last modified July 15 19:27 EDT 2024. Contains 374334 sequences. (Running on oeis4.)