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A084761
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Primes such that {a(m)-a(m-1)}/{a(m-1)-a(m-2)} is a unique integer.
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0
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2, 3, 5, 7, 13, 37, 157, 877, 6637, 46957, 530797, 4885357, 61494637, 684196717, 6911217517, 94089508717, 1576120459117, 23806584715117, 468415869835117, 11583647997835117, 211657826301835117, 3412844679165835117
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The sequence of successive difference ratios {a(m)-a(m-1)}/{a(m-1)-a(m-2)} is 2,1,3,4,5,6,8,7,... Conjecture:(1) every number is a term of this sequence, or for every number r there exists some k such that {a(k) - a(k-1)}/{a(k-1)-a(k-2)}= r. Question: What is the longest string of consecutive integers in this sequence ( of successive differences)?
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EXAMPLE
| {a(5)-a(4)}/{a(4)-a(3) =(13-7)/(7-5) = 3. Then it is to be taken care of that this ratio is not 3 for any other set of three successive terms.
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CROSSREFS
| Sequence in context: A050779 A052291 A072826 * A038965 A055694 A007311
Adjacent sequences: A084758 A084759 A084760 * A084762 A084763 A084764
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jun 17 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jan 06 2005
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