login
A279272
Numbers k such that k^7 - 1 and k^7 + 1 are semiprimes.
0
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
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
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Dec 09 2016
EXTENSIONS
More terms from Jon E. Schoenfield, Dec 14 2016
STATUS
approved