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A365200
Even semiprimes that are the exact average of two consecutive odd semiprimes.
2
34, 86, 94, 122, 142, 194, 202, 214, 218, 262, 302, 314, 358, 386, 394, 422, 446, 562, 586, 626, 634, 698, 734, 838, 842, 922, 982, 1042, 1138, 1234, 1262, 1306, 1346, 1366, 1402, 1522, 1642, 1646, 1658, 1754, 1762, 1774, 1838, 1874, 1894, 1906, 1942, 1982, 2026, 2098, 2102, 2182, 2186, 2218
OFFSET
1,1
EXAMPLE
34 is a term because (33 + 35)/2 = 34 = 2*17 is an even semiprime.
86 is a term because (85 + 87)/2 = 86 = 2*43 is an even semiprime.
MATHEMATICA
sp=Select[Range[5, 2400, 2], PrimeOmega[#]==2&]; a={}; For[i=1, i<Length[sp], i++, hav=Sum[Part[sp, k], {k, i, i+1}]/4; If[PrimeQ[hav], AppendTo[a, 2hav]]]; a (* Stefano Spezia, Aug 25 2023 *)
PROG
(PARI) upto(n) = {my(res = List(), l = List([0, 9]), s = sum(i = 1, #l, l[i]), i = l[#l]+2, ntimes2 = 2*n); while(1, if(bigomega(i) == 2, s += (i-l[1]); if(s > ntimes2, return(res)); if(s % 4 == 0 && isprime(s/4), listput(res, s/2)); listpop(l, 1); listput(l, i)); i+=2)} \\ David A. Corneth, Aug 26 2023
CROSSREFS
Subset of A100484.
Sequence in context: A260276 A278311 A213025 * A086005 A169834 A248201
KEYWORD
nonn
AUTHOR
Elmo R. Oliveira, Aug 25 2023
STATUS
approved