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Search: id:A122535
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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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+0
2
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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; listen)
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OFFSET
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1,1
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COMMENT
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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
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FORMULA
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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
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EXAMPLE
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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
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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]
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CROSSREFS
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Cf. A102552, A062839.
Adjacent sequences: A122532 A122533 A122534 this_sequence A122536 A122537 A122538
Sequence in context: A141850 A003551 A054643 this_sequence A058427 A142293 A052187
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KEYWORD
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nonn
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Sep 18 2006
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EXTENSIONS
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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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