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   A257309 Perfect hyper-4 powers: a^^b, where b <> 1. 4
   0, 1, 4, 16, 27, 256, 3125, 46656, 65536, 823543, 16777216, 387420489, 10000000000, 285311670611, 7625597484987, 8916100448256, 302875106592253, 11112006825558016, 437893890380859375, 18446744073709551616, 827240261886336764177, 39346408075296537575424, 1978419655660313589123979, 104857600000000000000000000 (list; graph; refs; listen; history; text; internal format)
   OFFSET 1,3 COMMENTS a^^b is the right associative power tower a^a^...^a^a of height b. a^^-1= 0 and a^^0 = 1. We exclude b=1 because otherwise all natural numbers would be in the sequence. LINKS EXAMPLE Numbers written as power towers include: 5^^2 = 5^5 = 3125; 3^^3 = 3^3^3 = 3^27 = 7625597484987; 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536; 0^^5 = 0^0^0^0^0 = 0^0^0^1 = 0^0^0 = 0^1 = 0; CROSSREFS Cf. A004231, A002488. Sequence in context: A111260 A067688 A097374 * A271936 A046358 A046366 Adjacent sequences: A257306 A257307 A257308 * A257310 A257311 A257312 KEYWORD nonn AUTHOR Natan Arie Consigli, May 07 2015 STATUS approved
  
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  Last modified November 26 13:43 EST 2022. Contains 358362 sequences. (Running on oeis4.)
explanation: The provided text is an excerpt from the Online Encyclopedia of Integer Sequences (OEIS) describing the sequence A257309, which lists perfect hyper-4 powers. The text includes a definition, examples, and references but does not contain a specific math question or an answer to a question.
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 is supported by the many generous donors to the OEIS Foundation.
  
   Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
   Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
   A257309 Perfect hyper-4 powers: a^^b, where b <> 1. 4
   0, 1, 4, 16, 27, 256, 3125, 46656, 65536, 823543, 16777216, 387420489, 10000000000, 285311670611, 7625597484987, 8916100448256, 302875106592253, 11112006825558016, 437893890380859375, 18446744073709551616, 827240261886336764177, 39346408075296537575424, 1978419655660313589123979, 104857600000000000000000000 (list; graph; refs; listen; history; text; internal format)
   OFFSET 1,3 COMMENTS a^^b is the right associative power tower a^a^...^a^a of height b. a^^-1= 0 and a^^0 = 1. We exclude b=1 because otherwise all natural numbers would be in the sequence. LINKS EXAMPLE Numbers written as power towers include: 5^^2 = 5^5 = 3125; 3^^3 = 3^3^3 = 3^27 = 7625597484987; 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536; 0^^5 = 0^0^0^0^0 = 0^0^0^1 = 0^0^0 = 0^1 = 0; CROSSREFS Cf. A004231, A002488. Sequence in context: A111260 A067688 A097374 * A271936 A046358 A046366 Adjacent sequences: A257306 A257307 A257308 * A257310 A257311 A257312 KEYWORD nonn AUTHOR Natan Arie Consigli, May 07 2015 STATUS approved
  
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  Last modified November 26 13:43 EST 2022. Contains 358362 sequences. (Running on oeis4.)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an excerpt from the Online Encyclopedia of Integer Sequences (OEIS) describing the sequence A257309, which lists perfect hyper-4 powers. The text includes a definition, examples, and references but does not contain a specific math question or an answer to a question.
  
  Label: no-question