OFFSET
1,1
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
KEYWORD
nonn
AUTHOR
Elmo R. Oliveira, Aug 25 2023
STATUS
approved