This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A133795 #10 Sep 06 2024 18:47:31
%S A133795 5,8,12,15,21,23,32,34,38,42,50,52,54,58,62,70,76,79,84,87,89,94,101,
%T A133795 106,114,118,124,128,130,132,138,141,144,147,159,165,171,177,179,182,
%U A133795 185,187,195,200,202,211,213,215,218,221,231,236,238,241,247,252,261
%N A133795 a(n) = n-th semiprime + n-th non-semiprime.
%C A133795 Semiprime analog of A022797 n-th prime + n-th nonprime. a(n) is prime for n = 1, 6, 18, 21, 23. a(n) is itself semiprime for n = 4, 5, 22, 25, 38, 39, 57, 62, 69, 77 of which first 10 indices all but n=5 are themselves semiprimes.
%F A133795 a(n) = A001358(n) + A100959(n).
%e A133795 a(1) = 1st semiprime + 1st nonsemiprime = 4 + 1 = 5.
%e A133795 a(2) = 2nd semiprime + 2nd nonsemiprime = 6 + 2 = 8.
%e A133795 a(3) = 3rd semiprime + 3rd nonsemiprime = 9 + 3 = 12.
%p A133795 A100959 := proc(n) option remember; local a ; if n = 1 then 1 ; else for a from A100959(n-1)+1 do if numtheory[bigomega](a) <> 2 then RETURN(a) ; fi ; od: fi ; end: A001358 := proc(n) option remember ; local a ; if n = 1 then 4 ; else for a from A001358(n-1)+1 do if numtheory[bigomega](a) = 2 then RETURN(a) ; fi ; od: fi ; end: A133795 := proc(n) A100959(n)+A001358(n) ; end: seq(A133795(n),n=1..100) ; # _R. J. Mathar_, Jan 09 2008
%t A133795 Module[{nn=200,spr,non},spr=Select[Range[nn],PrimeOmega[#]==2&];non=Take[ Complement[ Range[ nn],spr],Length[ spr]];Total/@Thread[{spr,non}]] (* _Harvey P. Dale_, Sep 06 2024 *)
%Y A133795 Cf. A000040, A001358, A022797, A100959.
%K A133795 easy,nonn,less
%O A133795 1,1
%A A133795 _Jonathan Vos Post_, Jan 05 2008
%E A133795 Corrected and extended by _R. J. Mathar_, Jan 09 2008