A365202 Even semiprimes that are the exact average of six consecutive odd semiprimes.

146, 194, 302, 478, 482, 614, 706, 1006, 1438, 1966, 1994, 2186, 2206, 2426, 2462, 2594, 2614, 3098, 3274, 3518, 3742, 3986, 4282, 4406, 4594, 4702, 5354, 5606, 6038, 6178, 6218, 6238, 6442, 6626, 6782, 7262, 7642, 7646, 7886, 8254, 9098, 9194, 9298, 9346, 9442, 9574, 9938

Offset: 1

Author

Elmo R. Oliveira, Aug 25 2023

Keywords

• nonn

Examples

			146 is a term because (133 + 141 + 143 + 145 + 155 + 159)/6 = 146 = 2*73 is an even semiprime.
302 is a term because (295 + 299 + 301 + 303 + 305 + 309)/6 = 302 = 2*151 is an even semiprime.
		

Crossrefs

Cf. A046315, A365200, A365201.

Subset of A100484.

Programs

Mathematica

sp=Select[Range[5,12000,2], PrimeOmega[#]==2&]; a={}; For[i=1, iStefano Spezia, Aug 25 2023 *)

PARI

upto(n) = {my(res = List(), l = List([0,9,15,21,25,33]), s = sum(i = 1, #l, l[i]), i = l[#l]+2, ntimes6 = 6*n); while(1, if(bigomega(i) == 2, s += (i-l[1]); if(s > ntimes6, return(res)); if(s % 12 == 0 && isprime(s/12), listput(res, s/6)); listpop(l, 1); listput(l, i)); i+=2)} \\ David A. Corneth, Aug 26 2023