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.

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

K. D. Bajpai, Table of n, a(n) for n = 1..14530

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

Cf. A001358, A162861, A245393.

Sequence in context: A187436 A193055 A240099 * A015388 A257714 A204668

Adjacent sequences: A245480 A245481 A245482 * A245484 A245485 A245486

Keyword

nonn

Author

K. D. Bajpai, Jul 23 2014

Status

approved