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A122535
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Smallest prime of a triple of successive primes, where the middle one is the arithmetic mean of the other two.
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7
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3, 47, 151, 167, 199, 251, 257, 367, 557, 587, 601, 647, 727, 941, 971, 1097, 1117, 1181, 1217, 1361, 1499, 1741, 1747, 1901, 2281, 2411, 2671, 2897, 2957, 3301, 3307, 3631, 3727, 4007, 4397, 4451, 4591, 4651, 4679, 4987, 5101, 5107, 5297, 5381, 5387
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Subsets are A047948, A052188, A052189, A052190, A052195, A052197, A052198, etc. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 11 2008
Could be generated by searching for cases A001223(i)=A001223(i+1), writing down A000040(i). - R. J. Mathar, Dec 20 2008
Contribution from Carmine Suriano (surianonoi5(AT)libero.it), Sep 05 2010: (Start)
Each term is a prime obtained as the average of three consecutive primes:
a(n)=[p(n-1)+p(n)+p(n+1)]/3 (End)
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| 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]
{A000040(i): A000040(i+1)= (A000040(i)+A000040(i+2))/2 } - R. J. Mathar, Dec 20 2008
a(n) = A000040(A064113(n)). [Reinhard Zumkeller, Jan 20 2012]
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EXAMPLE
| 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.
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.
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MATHEMATICA
| 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]
Transpose[Select[Partition[Prime[Range[750]], 3, 1], #[[2]]==(#[[1]]+#[[3]])/2&]][[1]] [From Harvey P. Dale, Jan. 9, 2011]
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PROG
| (Haskell)
a122535 = a000040 . a064113 -- Reinhard Zumkeller, Jan 20 2012
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CROSSREFS
| Cf. A102552, A062839.
Cf. A006562, A181424.
Sequence in context: A141850 A003551 A054643 * A058427 A142293 A052187
Adjacent sequences: A122532 A122533 A122534 * A122536 A122537 A122538
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KEYWORD
| nonn
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AUTHOR
| Miklos Kristof (kristmikl(AT)freemail.hu), Sep 18 2006
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EXTENSIONS
| More terms from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 13 2008
Rephrased definition. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 20 2008
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