A365201 - OEIS

A365201

Even semiprimes that are the exact average of four consecutive odd semiprimes.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..50.

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

Cf. A046315, A365200, A365202.

Subset of A100484.

Sequence in context: A300379 A300681 A309143 * A044325 A044706 A217991

Adjacent sequences: A365198 A365199 A365200 * A365202 A365203 A365204

KEYWORD

nonn

AUTHOR

Elmo R. Oliveira, Aug 25 2023

STATUS

approved