A364321 -id:A364321 - cp's OEIS frontend

A364320 Prime numbers that are the exact average of eight consecutive odd semiprimes.

43, 317, 607, 719, 853, 887, 919, 1231, 1237, 1283, 1303, 1951, 2179, 2609, 3001, 3271, 3389, 3491, 3547, 3643, 3889, 3931, 4241, 4297, 4447, 4517, 4567, 4621, 4817, 4831, 4871, 4909, 5479, 5623, 5647, 5653, 5953, 6211, 6301, 6869, 7019, 7559, 8011, 8191, 8297, 8311, 8317, 8369, 8447

Offset: 1

Elmo R. Oliveira, Sep 25 2023

nonn

			43 is a term because (25 + 33 + 35 + 39 + 49 + 51 + 55 + 57)/8 = 43 is prime.
719 is a term because (703 + 707 + 713 + 717 + 721 + 723 + 731 + 737)/8 = 719 is prime.

Cf. A000040, A046315.

Cf. A363074, A363187, A363188, A364147, A364148, A364149, A364321, A364689.

Select[Mean /@ Partition[Select[Range[1, 9000, 2], PrimeOmega[#] == 2 &], 8, 1], PrimeQ] (* Amiram Eldar, Sep 25 2023 *)

A364689 Prime numbers that are the exact average of ten consecutive odd semiprimes.

Original entry on oeis.org

43, 53, 73, 83, 113, 373, 449, 577, 971, 1259, 1327, 1381, 1499, 1543, 1847, 2239, 2311, 2339, 2351, 2383, 2953, 3109, 3257, 3389, 4021, 4297, 4919, 5101, 5227, 5591, 5701, 5737, 5927, 6733, 6907, 7109, 7253, 7823, 8011, 9137, 9403, 9613, 10177, 11471, 11621, 11677, 12251, 12479, 12671, 12781

Offset: 1

Elmo R. Oliveira, Sep 25 2023

nonn

			43 is a term because (21 + 25 + 33 + 35 + 39 + 49 + 51 + 55 + 57 + 65)/10 = 43 is prime.
449 is a term because (417 + 427 + 437 + 445 + 447 + 451 + 453 + 469 + 471 + 473)/10 = 449 is prime.

Cf. A000040, A046315.

Cf. A363074, A363187, A363188, A364147, A364148, A364149, A364320, A364321.

Select[Mean /@ Partition[Select[Range[1, 13000, 2], PrimeOmega[#] == 2 &], 10, 1], PrimeQ] (* Amiram Eldar, Sep 25 2023 *)

cp's OEIS Frontend

A364320 Prime numbers that are the exact average of eight consecutive odd semiprimes.

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