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A181994 Initial members of prime triples p < q < r such that r-q = n*(q-p). 2

%I

%S 3,2,29,8117,137,197,45433,1931,521,156151,1949,1667,480203,2969,7757,

%T 2181731,12161,28349,6012893,20807,16139,3933593,163061,86627,

%U 13626251,25469,40637,60487753,79697,149627,217795241,625697,552401,240485251,173357,360089,122164741

%N Initial members of prime triples p < q < r such that r-q = n*(q-p).

%C For some n, a(n) are abnormally large: note, e.g., that if q-p=2, then n cannot be of the form 4+3k, that is why a(4), a(7), a(10), ... are larger than neighbor terms; also, a(67) > 1.1*10^11. Is the sequence infinite?

%H Zak Seidov, <a href="/A181994/b181994.txt">Table of n, a(n) for n = 1..66</a>

%F a(n) = prevprime(A179210(n)). - _Robert G. Wilson v_, Dec 23 2016

%e First 10 cases of {n,p,q,r}: {1,3,5,7}, {2,2,3,5}, {3,29,31,37}, {4,8117,8123,8147}, {5,137,139,149}, {6,197,199,211}, {7,45433,45439,45481}, {8,1931,1933,1949}, {9,521,523,541}, {10,156151,156157,156217}.

%Y Particular cases with q-p=2: A022004 [(r-q)=2*(q-p)], A049437 [r-q)=3*(q-p) starting with 2nd term].

%Y Cf. A179210.

%K nonn

%O 1,1

%A _Zak Seidov_, May 31 2012

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Last modified June 19 23:27 EDT 2021. Contains 345154 sequences. (Running on oeis4.)