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%I #7 Aug 23 2014 14:26:03
%S 2,3,5,7,13,37,157,877,6637,46957,530797,4885357,61494637,684196717,
%T 6911217517,94089508717,1576120459117,23806584715117,468415869835117,
%U 11583647997835117,211657826301835117,3412844679165835117
%N Primes such that {a(m)-a(m-1)}/{a(m-1)-a(m-2)} is a unique integer.
%C 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)?
%e {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.
%K nonn
%O 0,1
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 17 2003
%E More terms from _David Wasserman_, Jan 06 2005
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