A245483 - OEIS

%I #15 Oct 10 2018 11:54:27

%S 44287,838861,247165843,3138105961,269971011311,540609741211,

%T 1034834473201,3382547898907,5824512944911,9752380952381,

%U 25405143539623,91699453500601,406683658856861,794014903012651,2005395532515211,7936895933061811,10230009756097561,13103072183720201

%N Semiprimes of the form m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1.

%C All the terms in sequence are odd semiprimes, but none is congruent to 5 or 9 (mod 10).

%H K. D. Bajpai, <a href="/A245483/b245483.txt">Table of n, a(n) for n = 1..14530</a>

%e m = 3: m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 = 44287 = 67 * 661, which is semiprime and appears in the sequence.

%e m = 7: m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 = 247165843 = 23 * 10746341, which is semiprime and appears in the sequence.

%t A245483 = {}; k = n^10 - n^9 + n^8 - n^7 + n^6 - n^5 + n^4 - n^3 + n^2 - n + 1; Do[If[PrimeOmega[k] == 2, AppendTo[A245483, k]], {n, 100}]; A245483

%t Select[Table[1-n+n^2-n^3+n^4-n^5+n^6-n^7+n^8-n^9+n^10,{n,100}],PrimeOmega[ #] ==2&] (* _Harvey P. Dale_, Oct 10 2018 *)

%o (PARI)

%o for(n=1,10^3,s=sum(i=0,10,(-n)^i);if(bigomega(s)==2,print1(s,", "))) \\ _Derek Orr_, Aug 03 2014

%Y Cf. A001358, A162861, A245393.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Jul 23 2014