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A345363

Composite numbers that are the exact average of three consecutive primes.

511, 537, 999, 1073, 1239, 1461, 1501, 1541, 1763, 1773, 1899, 1917, 2071, 2181, 2401, 2409, 2449, 3059, 3069, 3179, 3201, 3509, 3807, 4081, 4101, 4179, 4387, 4399, 4437, 4467, 4559, 4607, 4681, 4705, 4879, 5089, 5211, 5257, 5271, 5373, 5429, 5757, 5829, 6415, 6621, 6671

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OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..5000

EXAMPLE

511 is composite and the average of the consecutive primes 503, 509 and 521. Thus, 511 is in the sequence.

MATHEMATICA

Select[Table[(Prime[n] + Prime[n + 1] + Prime[n + 2])/3, {n, 2000}], IntegerQ[#] && ! PrimeQ[#] &]

Select[Mean/@Partition[Prime[Range[1000]], 3, 1], IntegerQ[#]&&CompositeQ[#]&] (* Harvey P. Dale, Feb 01 2025 *)

CROSSREFS

Cf. A242218 (subsequence of semiprimes).