A279272 Numbers k such that k^7 - 1 and k^7 + 1 are semiprimes.

72, 282, 9000, 13932, 19212, 22158, 49920, 65538, 72228, 78888, 144408, 169320, 201492, 201828, 218460, 234540, 270030, 296478, 325080, 355008, 365748, 411000, 448872, 461052, 484152, 504618, 555522, 558252, 586362, 622620, 674058, 981810, 1067490, 1095792

Offset

1,1

Comments

Since k^7 - 1 = (k-1)*(k^6 + k^5 + k^4 + k^3 + k^2 + k + 1) and k^7 + 1 = (k+1)*(k^6 - k^5 + k^4 - k^3 + k^2 - k + 1) (and since there is no term less than 3, so k-1 must have at least one prime factor), this sequence lists the numbers k such that k-1, k+1, k^6 + k^5 + k^4 + k^3 + k^2 + k + 1, and k^6 - k^5 + k^4 - k^3 + k^2 - k + 1 are all prime. - Jon E. Schoenfield, Dec 14 2016

Links

Table of n, a(n) for n=1..34.

Mathematica

Select[Range[100000], PrimeOmega[#^7 - 1] == PrimeOmega[#^7 + 1]== 2 &]

Prog

(Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [n: n in [4..10000] | IsSemiprime(n^7-1)and IsSemiprime(n^7+1)]

Crossrefs

Cf. A105041, A108278, A261436, A268043, A276905.

Sequence in context: A305222 A316800 A004007 * A378002 A173546 A308136

Adjacent sequences: A279269 A279270 A279271 * A279273 A279274 A279275

Keyword

nonn

Author

Vincenzo Librandi, Dec 09 2016

Extensions

More terms from Jon E. Schoenfield, Dec 14 2016

Status

approved