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%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