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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 (list; graph; refs; listen; history; text; internal format)
   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
  
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  Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)
explanation: The provided text is an entry from the On-Line Encyclopedia of Integer Sequences (OEIS) describing the sequence A245483. This sequence lists semiprimes of the form \( m^{10} - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 \). The entry includes the first few terms of the sequence, a comment about the properties of the terms, examples, Mathematica and PARI code for generating the sequence, and cross-references to related sequences.
  
  The text does not contain a specific math question or a question and answer. It is primarily a descriptive entry about a particular sequence.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
  
   Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
   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 (list; graph; refs; listen; history; text; internal format)
   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
  
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  Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an entry from the On-Line Encyclopedia of Integer Sequences (OEIS) describing the sequence A245483. This sequence lists semiprimes of the form \( m^{10} - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 \). The entry includes the first few terms of the sequence, a comment about the properties of the terms, examples, Mathematica and PARI code for generating the sequence, and cross-references to related sequences.
  
  The text does not contain a specific math question or a question and answer. It is primarily a descriptive entry about a particular sequence.
  
  Label: no-question