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Search: id:A075541
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| A075541 |
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Indices of primes p(i) such that (1/3) (p(i)+p(i+1)+p(i+2)) is an integer. |
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3
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| 2, 15, 36, 39, 46, 54, 55, 73, 96, 99, 102, 107, 110, 118, 129, 160, 164, 167, 179, 184, 187, 194, 199, 202, 218, 231, 238, 239, 242, 271, 272, 273, 274, 290, 291, 292, 311, 326, 339, 356, 357, 358, 362, 387, 419, 426, 437, 438, 449, 452, 464, 465, 489, 508
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Not every three successive primes have an integer average. The integer averages are in A075540.
Not all of these 3-averages are prime: the prime 3-averages are in A006562 (balanced primes). There are suprisingly many prime 3-averages: among first 117 3-averages, there are 59 primes. Indices i(n) of first prime in sequence of three primes with integer average are in sequence A064113. Interprimes (s-averages with s=2) are all composite, see A024675.
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FORMULA
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i(n)-> 1/3 (p(i)+p(i+1)+p(i+2)) is integer.
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EXAMPLE
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i(2) = 15 because (p(15)+p(16)+p(17)) = 1/3(47 + 53 + 59)=53 (integer average of three successive primes).
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MATHEMATICA
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A075541= {}; Do[If[IntegerQ[s3 = (Prime[i] + Prime[i + 1] + Prime[i + 2])/3], A075541 = Append[A075541, i]], {i, 1000}]; (* 119 terms*)
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CROSSREFS
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Cf. A006562, A024675, A075540, A064113.
Sequence in context: A154790 A042461 A045486 this_sequence A075542 A064113 A007217
Adjacent sequences: A075538 A075539 A075540 this_sequence A075542 A075543 A075544
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Sep 21 2002
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