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%I #19 Dec 11 2016 16:15:10
%S 5,11,29,6421,149,521,84913,1949,1277,43391,1151,4547,933151,2999,
%T 6947,1568867,10007,32297,4131223,25301,78779,12809491,91079,28277,
%U 13626407,35729,117497,37305881,399851,102761,217795433,288647,296909,240485461,173429,1026029,213158501,1053179,371027,1163010421,1885151,461801,1661688551,1155821,576881,3403741987,4876607,4252679,10394432611,838349,1775171
%N a(n) is the smallest prime q such that (q-p)/(r-q) = n, where p<q<r are consecutive primes (or 0 if none exist).
%C Conjecture: a(n)>0 for n >= 1.
%C It would appear that a(3n+1) is greater than either a(3n) or a(3n+2).
%C Records appear for a(n) for n's: 1, 2, 3, 4, 7, 13, 16, 19, 22, 25, 28, 31, 34, 40, 43, 46, 49, ..., .
%H Robert G. Wilson v, <a href="/A179256/b179256.txt">Table of n, a(n) for n = 1..57</a>
%t f[n_] := f[n] = Block[{p = 3, q = 5, r = 7}, While[p + n*r != (n + 1) q, p = q; q = r; r = NextPrime@ r]; q]; Array[f, 33]
%t p = 2; q = 3; r = 5; t[_] = 0; While[p < 10^9, If[ Mod[q - p, r - q] == 0 && t[(q - p)/(r - q)] == 0, t[(q - p)/(r - q)] = q; Print[{(q - p)/(r - q), q}]]; p = q; q = r; r = NextPrime@ r]; t@# & /@ Range@45 (* _Robert G. Wilson v_, Dec 10 2016 *)
%Y Cf. A179210, A179234, A168253, A001223
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Jan 05 2011
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