A365200 Even semiprimes that are the exact average of two consecutive odd semiprimes.

34, 86, 94, 122, 142, 194, 202, 214, 218, 262, 302, 314, 358, 386, 394, 422, 446, 562, 586, 626, 634, 698, 734, 838, 842, 922, 982, 1042, 1138, 1234, 1262, 1306, 1346, 1366, 1402, 1522, 1642, 1646, 1658, 1754, 1762, 1774, 1838, 1874, 1894, 1906, 1942, 1982, 2026, 2098, 2102, 2182, 2186, 2218

Offset: 1

Author

Elmo R. Oliveira, Aug 25 2023

Keywords

• nonn

Examples

			34 is a term because (33 + 35)/2 = 34 = 2*17 is an even semiprime.
86 is a term because (85 + 87)/2 = 86 = 2*43 is an even semiprime.
		

Crossrefs

Cf. A046315, A365201, A365202.

Subset of A100484.

Programs

Mathematica

sp=Select[Range[5,2400,2], PrimeOmega[#]==2&]; a={}; For[i=1, iStefano Spezia, Aug 25 2023 *)

PARI

upto(n) = {my(res = List(), l = List([0, 9]), s = sum(i = 1, #l, l[i]), i = l[#l]+2, ntimes2 = 2*n); while(1, if(bigomega(i) == 2, s += (i-l[1]); if(s > ntimes2, return(res)); if(s % 4 == 0 && isprime(s/4), listput(res, s/2)); listpop(l, 1); listput(l, i)); i+=2)} \\ David A. Corneth, Aug 26 2023