%I A122535
%S A122535 3,47,151,167,199,251,257,367,557,587,601,647,727,941,971,1097,1117,
%T A122535 1181,1217,1361,1499,1741,1747,1901,2281,2411,2671,2897,2957,3301,3307,
%U A122535 3631,3727,4007,4397,4451,4591,4651,4679,4987,5101,5107,5297,5381,5387
%N A122535 Smallest prime of a triple of successive primes, where the middle one 
               is the arithmetic mean of the other two.
%C A122535 Subsets are A047948, A052188, A052189, A052190, A052195, A052197, A052198, 
               etc. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 11 2008
%C A122535 Could be generated by searching for cases A001223(i)=A001223(i+1), writing 
               down A000040(i). - R. J. Mathar, Dec 20 2008
%F A122535 a(n)=If[(-Prime[n] + 2 Prime[1 + n] - Prime[2 + n])/((1 - Prime[n] +Prime[1 
               + n])^(3/2))==0,Prime[n]] [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), 
               Nov 13 2008]
%F A122535 {A000040(i): A000040(i+1)= (A000040(i)+A000040(i+2))/2 } - R. J. Mathar, 
               Dec 20 2008
%e A122535 The prime 7 is not in the list, because in the triple (7,11,13) of successive 
               primes, 11 is not equal (7+13)/2=10.
%e A122535 The second term, 47, is the first prime in the triple (47,53,59) of primes, 
               where 53 is the mean of 47 and 59.
%t A122535 Clear[d2, d1, k]; d2[n_] = Prime[n + 2] - 2*Prime[n + 1] + Prime[n]; 
               d1[n_] = Prime[n + 1] - Prime[n]; k[n_] = -d2[n]/(1 + d1[n])^(3/2); 
               Flatten[Table[If[k[n] == 0, Prime[n], {}], {n, 1, 1000}]] [From Roger 
               L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 13 2008]
%Y A122535 Cf. A102552, A062839.
%Y A122535 Sequence in context: A141850 A003551 A054643 this_sequence A058427 A142293 
               A052187
%Y A122535 Adjacent sequences: A122532 A122533 A122534 this_sequence A122536 A122537 
               A122538
%K A122535 nonn
%O A122535 1,1
%A A122535 Miklos Kristof (kristmikl(AT)freemail.hu), Sep 18 2006
%E A122535 More terms from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 13 2008
%E A122535 Rephrased definition. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Dec 20 2008