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

1,1

Links

Table of n, a(n) for n=1..47.

Example

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.

Mathematica

sp=Select[Range[5, 12000, 2], PrimeOmega[#]==2&]; a={}; For[i=1, i<Length[sp]-5, i++, hav=Sum[Part[sp, k], {k, i, i+5}]/12; If[PrimeQ[hav], AppendTo[a, 2hav]]]; a (* Stefano Spezia, Aug 25 2023 *)

Prog

(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

Crossrefs

Cf. A046315, A365200, A365201.

Subset of A100484.

Sequence in context: A145915 A248406 A135666 * A119379 A118699 A238579

Adjacent sequences: A365199 A365200 A365201 * A365203 A365204 A365205

Keyword

nonn

Author

Elmo R. Oliveira, Aug 25 2023

Status

approved