A261436 Numbers k such that k^7-1 is a semiprime.

3, 6, 14, 38, 60, 68, 72, 80, 128, 158, 180, 192, 264, 282, 294, 350, 450, 464, 548, 660, 710, 734, 798, 822, 878, 912, 942, 984, 998, 1052, 1188, 1194, 1224, 1280, 1284, 1382, 1424, 1482, 1494, 1512, 1550, 1554, 1572, 1608, 1622, 1668, 1700, 1710, 1790, 1802

Offset

1,1

Comments

Numbers k such that k-1 and k^6+k^5+k^4+k^3+k^2+k+1 are both prime.

Intersection of A008864 and A100330. - Michel Marcus, Aug 21 2015

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

3 is in sequence because 3^7-1 = 2186 = 2*1093, where 2 and 1093 are both prime.

Maple

with(numtheory): A261436:=n->`if`(bigomega(n^7-1)=2, n, NULL): seq(A261436(n), n=1..2000); # Wesley Ivan Hurt, Aug 21 2015
select(n -> isprime(n-1) and isprime(n^6+n^5+n^4+n^3+n^2+n+1), [3, (2*i $i=2..10000)]); # Robert Israel, Aug 21 2015

Mathematica

Select[Range[5000], PrimeOmega[#^7 - 1] == 2 &]

Prog

(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..5000] | IsSemiprime(s) where s is n^7- 1];
(PARI)  isok(n)=bigomega(n^7-1)==2 \\ Anders Hellström, Aug 21 2015

Crossrefs

Cf. similar sequences listed in A261435.

Cf. A105041.

Cf. A008864, A100330.

Sequence in context: A100446 A106395 A369544 * A335580 A079003 A099966

Adjacent sequences: A261433 A261434 A261435 * A261437 A261438 A261439

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 21 2015

Status

approved