A276905 -id:A276905 - cp's OEIS frontend

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

Vincenzo Librandi, Dec 09 2016

nonn

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

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

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

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

More terms from Jon E. Schoenfield, Dec 14 2016

cp's OEIS Frontend

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

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