A364147 - OEIS

%I #12 Aug 12 2023 00:43:34

%S 101,677,743,811,907,1039,1109,1129,1301,1373,1381,1567,1789,1931,

%T 1949,1979,2029,2447,2621,2663,2731,2879,2909,2971,3119,3187,3221,

%U 3319,3529,3631,3677,3803,3823,3943,4201,4253,4549,4597,4637,4643,4649,4801,4951,5119,5189,5431,5987,6053,6151,6311

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

%H Robert Israel, <a href="/A364147/b364147.txt">Table of n, a(n) for n = 1..10000</a>

%e 101 is a term because (91 + 93 + 95 + 111 + 115)/5 = 101 is prime.

%e 743 is a term because (737 + 737 + 745 + 749 + 753)/5 = 743 is prime.

%p N:= 10^4: # for terms involving semiprimes up to N

%p OSP:= select(t -> numtheory:-bigomega(t) = 2, [seq(i,i=1..N,2)]):

%p select(t -> t::integer and isprime(t), add(OSP[i..-6+i],i=1..5)/5); # _Robert Israel_, Aug 11 2023

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

%Y Cf. A000040, A046315.

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

%K nonn

%O 1,1

%A _Elmo R. Oliveira_, Jul 10 2023