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A066875
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Numbers n such that prime(n+1) + prime(n-1) = 2*prime(n).
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3
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3, 16, 37, 40, 47, 55, 56, 74, 103, 108, 111, 119, 130, 161, 165, 185, 188, 195, 200, 219, 240, 272, 273, 292, 340, 359, 388, 420, 427, 465, 466, 509, 521, 554, 600, 606, 622, 630, 634, 668, 683, 684, 703, 710, 711, 734, 762, 792, 814, 822, 823, 830, 831, 883
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OFFSET
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1,1
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COMMENTS
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The indices of primes that are equidistant from the two primes surrounding them. - Harvey P. Dale, May 16 2013
Indices of balanced primes (A006562). - Zak Seidov, Mar 03 2019
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n) = PrimePi(A006562(n)) = A000720(A006562(n)).
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MATHEMATICA
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Select[Range[2, 1000], Prime[ # ] == (Prime[ # + 1] + Prime[ # - 1])/2 &] (* Ray Chandler, Jan 09 2007 *)
PrimePi/@Transpose[Select[Partition[Prime[Range[900]], 3, 1], Length[ Union[ Differences[ #]]]==1&]][[2]] (* Harvey P. Dale, May 16 2013 *)
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PROG
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(PARI) { n=0; for (m=2, 10^10, if (prime(m+1) + prime(m-1) == 2*prime(m), write("b066875.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Apr 03 2010
(Magma) [n: n in [2..1000] | 2*NthPrime(n) eq (NthPrime(n-1) + NthPrime(n+1))]; // Vincenzo Librandi, Apr 09 2015
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CROSSREFS
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Cf. A000720 (primepi), A006562 (balanced primes).
Sequence in context: A217130 A173390 A173891 * A294419 A196596 A196573
Adjacent sequences: A066872 A066873 A066874 * A066876 A066877 A066878
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre, Jan 21 2002
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EXTENSIONS
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Corrected by Ray Chandler, Jan 09 2007
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STATUS
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approved
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