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A245483
Semiprimes of the form m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1.
1
44287, 838861, 247165843, 3138105961, 269971011311, 540609741211, 1034834473201, 3382547898907, 5824512944911, 9752380952381, 25405143539623, 91699453500601, 406683658856861, 794014903012651, 2005395532515211, 7936895933061811, 10230009756097561, 13103072183720201
OFFSET
1,1
COMMENTS
All the terms in sequence are odd semiprimes, but none is congruent to 5 or 9 (mod 10).
LINKS
EXAMPLE
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.
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.
MATHEMATICA
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
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 *)
PROG
(PARI)
for(n=1, 10^3, s=sum(i=0, 10, (-n)^i); if(bigomega(s)==2, print1(s, ", "))) \\ Derek Orr, Aug 03 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Jul 23 2014
STATUS
approved