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A066875 Numbers n such that prime(n+1) + prime(n-1) = 2*prime(n). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The indices of primes that are equidistant from the two primes surrounding them. - Harvey P. Dale, May 16 2013

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = PrimePi(A006562(n)) = A000720(A006562(n)).

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A006562 (balanced primes).

Sequence in context: A217130 A173390 A173891 * A196596 A196573 A196804

Adjacent sequences:  A066872 A066873 A066874 * A066876 A066877 A066878

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jan 21 2002

EXTENSIONS

Corrected by Ray Chandler, Jan 09 2007

STATUS

approved

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Last modified December 7 11:15 EST 2016. Contains 278872 sequences.