A365201 Even semiprimes that are the exact average of four consecutive odd semiprimes.

74, 146, 194, 218, 302, 482, 586, 734, 746, 842, 914, 1042, 1138, 1262, 1346, 1438, 1574, 1646, 1654, 1838, 1874, 1894, 1906, 1942, 2026, 2186, 2206, 2458, 2462, 2762, 2906, 2962, 2974, 3098, 3106, 3202, 3218, 3826, 4198, 4274, 4286, 4322, 4414, 4502, 4534, 4622, 4666, 4754, 4934, 4946

Offset: 1

Author

Elmo R. Oliveira, Aug 25 2023

Keywords

• nonn

Examples

			74 is a term because (65 + 69 + 77 + 85)/4 = 74 = 2*37 is an even semiprime.
218 is a term because (215 + 217 + 219 + 221)/4 = 218 = 2*109 is an even semiprime.
		

Crossrefs

Cf. A046315, A365200, A365202.

Subset of A100484.

Programs

Mathematica

sp=Select[Range[5,5200,2], PrimeOmega[#]==2&]; a={}; For[i=1, iStefano Spezia, Aug 25 2023 *)

PARI

upto(n) = {my(res = List(), l = List([0, 9, 15, 21]), s = sum(i = 1, #l, l[i]), i = l[#l]+2, ntimes4 = 4*n); while(1, if(bigomega(i) == 2, s += (i-l[1]); if(s > ntimes4, return(res)); if(s % 8 == 0 && isprime(s/8), listput(res, s/4)); listpop(l, 1); listput(l, i)); i+=2)} \\ David A. Corneth, Aug 26 2023