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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 (list; graph; refs; listen; history; text; internal format)
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 * A173546 A308136 A242534

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

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Last modified November 19 16:37 EST 2019. Contains 329323 sequences. (Running on oeis4.)