text: The OEIS is supported by the many generous donors to the OEIS Foundation.
  
   Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
   A070899 a(1)=1, a(n) is the smallest integer > a(n-1) such that the largest element in the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) equals 3n. 0
   1, 6, 13, 16, 49, 71, 124, 188, 298, 326, 333, 354, 440, 797, 832, 954, 1006, 1040, 1280, 1319, 1414, 2038, 2113, 2231, 2291, 2924, 2973, 3107, 3983, 3984, 4331, 4605, 4763, 5756, 6314, 6325, 6402, 7501, 7967, 8073, 8143, 8895, 9567, 9900, 10333 (list; graph; refs; listen; history; text; internal format)
   OFFSET 1,2 COMMENTS sum(k=>1,1/a(k))=C=1.3... LINKS Table of n, a(n) for n=1..45. EXAMPLE The continued fraction for S(7)=1+1/6+1/13+1/16+1/49+1/71+1/124 is [1, 2, 1, 6, 1, 1, 2, 3, 3, 1, 21, 1, 1, 3, 1, 3, 18, 3] where the largest element is 21=3*7 and 124 is the smallest integer > a(6)=71 with this property, hence a(7)=124. PROG (PARI) s=1; t=1; for(n=1, 60, s=s+1/t; while(abs(3*n-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", ")) CROSSREFS Sequence in context: A053753 A228380 A090068 * A265756 A332988 A333011 Adjacent sequences: A070896 A070897 A070898 * A070900 A070901 A070902 KEYWORD easy,nonn AUTHOR Benoit Cloitre, May 19 2002 STATUS approved
  
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  Last modified September 10 16:36 EDT 2024. Contains 375791 sequences. (Running on oeis4.)
explanation: The provided text is an entry from the On-Line Encyclopedia of Integer Sequences (OEIS) for sequence A070899. It describes a sequence where each term is the smallest integer greater than the previous term such that the largest element in the simple continued fraction for the sum of the reciprocals of the terms up to that point equals 3 times the index of the term. The entry includes the sequence definition, initial terms, a comment, an example, a PARI program to generate the sequence, and cross-references.
  
  This text does not contain a specific math question or a question and answer. It is primarily a reference entry for a specific integer 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 is supported by the many generous donors to the OEIS Foundation.
  
   Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
   A070899 a(1)=1, a(n) is the smallest integer > a(n-1) such that the largest element in the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) equals 3n. 0
   1, 6, 13, 16, 49, 71, 124, 188, 298, 326, 333, 354, 440, 797, 832, 954, 1006, 1040, 1280, 1319, 1414, 2038, 2113, 2231, 2291, 2924, 2973, 3107, 3983, 3984, 4331, 4605, 4763, 5756, 6314, 6325, 6402, 7501, 7967, 8073, 8143, 8895, 9567, 9900, 10333 (list; graph; refs; listen; history; text; internal format)
   OFFSET 1,2 COMMENTS sum(k=>1,1/a(k))=C=1.3... LINKS Table of n, a(n) for n=1..45. EXAMPLE The continued fraction for S(7)=1+1/6+1/13+1/16+1/49+1/71+1/124 is [1, 2, 1, 6, 1, 1, 2, 3, 3, 1, 21, 1, 1, 3, 1, 3, 18, 3] where the largest element is 21=3*7 and 124 is the smallest integer > a(6)=71 with this property, hence a(7)=124. PROG (PARI) s=1; t=1; for(n=1, 60, s=s+1/t; while(abs(3*n-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", ")) CROSSREFS Sequence in context: A053753 A228380 A090068 * A265756 A332988 A333011 Adjacent sequences: A070896 A070897 A070898 * A070900 A070901 A070902 KEYWORD easy,nonn AUTHOR Benoit Cloitre, May 19 2002 STATUS approved
  
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  Last modified September 10 16:36 EDT 2024. Contains 375791 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) for sequence A070899. It describes a sequence where each term is the smallest integer greater than the previous term such that the largest element in the simple continued fraction for the sum of the reciprocals of the terms up to that point equals 3 times the index of the term. The entry includes the sequence definition, initial terms, a comment, an example, a PARI program to generate the sequence, and cross-references.
  
  This text does not contain a specific math question or a question and answer. It is primarily a reference entry for a specific integer sequence.
  
  Label: no-question