A365200 Even semiprimes that are the exact average of two consecutive odd semiprimes.

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

Links

Table of n, a(n) for n=1..54.

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

Cf. A046315, A365201, A365202.

Subset of A100484.

Sequence in context: A260276 A278311 A213025 * A086005 A169834 A248201

Adjacent sequences: A365197 A365198 A365199 * A365201 A365202 A365203

Keyword

nonn

Author

Elmo R. Oliveira, Aug 25 2023

Status

approved