A364147 Prime numbers that are the exact average of five consecutive odd semiprimes.

101, 677, 743, 811, 907, 1039, 1109, 1129, 1301, 1373, 1381, 1567, 1789, 1931, 1949, 1979, 2029, 2447, 2621, 2663, 2731, 2879, 2909, 2971, 3119, 3187, 3221, 3319, 3529, 3631, 3677, 3803, 3823, 3943, 4201, 4253, 4549, 4597, 4637, 4643, 4649, 4801, 4951, 5119, 5189, 5431, 5987, 6053, 6151, 6311

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

101 is a term because (91 + 93 + 95 + 111 + 115)/5 = 101 is prime.
743 is a term because (737 + 737 + 745 + 749 + 753)/5 = 743 is prime.

Maple

N:= 10^4: # for terms involving semiprimes up to N
OSP:= select(t -> numtheory:-bigomega(t) = 2, [seq(i, i=1..N, 2)]):
select(t -> t::integer and isprime(t), add(OSP[i..-6+i], i=1..5)/5); # Robert Israel, Aug 11 2023

Mathematica

Select[Mean /@ Partition[Select[Range[1, 6500, 2], PrimeOmega[#] == 2 &], 5, 1], PrimeQ] (* Amiram Eldar, Jul 11 2023 *)

Crossrefs

Cf. A000040, A046315.

Cf. A363074, A363187, A363188, A364148, A364149.

Sequence in context: A131697 A153806 A227521 * A171813 A089291 A167842

Adjacent sequences: A364144 A364145 A364146 * A364148 A364149 A364150

Keyword

nonn

Author

Elmo R. Oliveira, Jul 10 2023

Status

approved