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A084761
A sequence of primes such that {a(n)-a(n-1)}/{a(n-1)-a(n-2)} is a unique integer.
0
2, 3, 5, 7, 13, 37, 157, 877, 6637, 46957, 530797, 4885357, 61494637, 684196717, 6911217517, 94089508717, 1576120459117, 23806584715117, 468415869835117, 11583647997835117, 211657826301835117, 3412844679165835117
OFFSET
0,1
COMMENTS
The sequence of successive difference ratios {a(n)-a(n-1)}/{a(n-1)-a(n-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)?
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.
CROSSREFS
Sequence in context: A052291 A256072 A072826 * A038965 A295738 A265781
KEYWORD
nonn,more
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 17 2003
EXTENSIONS
More terms from David Wasserman, Jan 06 2005
STATUS
approved