A066875 Numbers k such that prime(k+1) + prime(k-1) = 2*prime(k).

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

Offset: 1

Author

Benoit Cloitre, Jan 21 2002

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A000720 (primepi), A006562 (balanced primes).

Programs

Magma

[n: n in [2..1000] | 2*NthPrime(n) eq (NthPrime(n-1) + NthPrime(n+1))]; // Vincenzo Librandi, Apr 09 2015

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 *)

PARI

isok(k) = { k > 1 && prime(k+1) + prime(k-1) == 2*prime(k) } \\ Harry J. Smith, Apr 03 2010

Formula

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

Extensions

Corrected by Ray Chandler, Jan 09 2007