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

Author

Vincenzo Librandi, Dec 09 2016

Keywords

• nonn

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

Crossrefs

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

Programs

Magma

IsSemiprime:=func; [n: n in [4..10000] | IsSemiprime(n^7-1)and IsSemiprime(n^7+1)];

Mathematica

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

Extensions

More terms from Jon E. Schoenfield, Dec 14 2016