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A365201
Even semiprimes that are the exact average of four consecutive odd semiprimes.
2
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
1,1
EXAMPLE
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.
MATHEMATICA
sp=Select[Range[5, 5200, 2], PrimeOmega[#]==2&]; a={}; For[i=1, i<Length[sp]-3, i++, hav=Sum[Part[sp, k], {k, i, i+3}]/8; 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]), 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
CROSSREFS
Subset of A100484.
Sequence in context: A300379 A300681 A309143 * A044325 A044706 A217991
KEYWORD
nonn
AUTHOR
Elmo R. Oliveira, Aug 25 2023
STATUS
approved