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

Author

Elmo R. Oliveira, Jul 10 2023

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A046315.

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

Programs

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 *)