A131109 - OEIS

%I #27 Mar 14 2024 15:21:40

%S 9,4,6,10,69,15,26,169,146,237,95,1082,818,597,1603,2705,2078,4511,

%T 1418,2681,14545,13863,37551,6559,16053,55805,26707,17965,308918,

%U 32777,41222,35103,393565,219509,153263,87627,2263057,35981,1789339,741841,797542

%N a(n) is the smallest semiprime such that difference between a(n) and next semiprime, b(n), is n.

%C This is the semiprime analogous to A000230. - _Robert G. Wilson v_, Jun 13 2013

%H Martin Raab, <a href="/A131109/b131109.txt">Table of n, a(n) for n = 1..120</a>, terms up to a(100) from T. D. Noe and Klaus Brockhaus

%F a(n) = A001358(A123375(n)). - _T. D. Noe_, Sep 28 2007

%e n, b(n)-a(n): 1=10-9, 2=6-4, 3=9-6, 4=14-10, 5=74-69, 6=21-15, 7=33-26, 8=177-169, 9=155-146, 10=247-237, 11=106-95, 12=1094-1082, 13=831-818, 14=611-597, 15=1618-1603, 16=2721-2705, 17=2095-2078, 18=4529-4511, 19=1437-1418, 20=2701-2681, 21=14566-14545, 22=13885-13863, 23=37574-37551, 24=6583-6559, 25=16078-16053, 26=55831-55805, 27=26734-26707, 28=17993-17965, 29=308947-308918, 30=32807-32777, 31=41253-41222, 32=35135-35103, 33=393598-393565, 34=219543-219509, 35=153298-153263, 36=87663-87627, 37=2263094-2263057, 38=36019-35981.

%t SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; NextSemiPrime[n_] := Module[{m = n + 1}, While[! SemiPrimeQ[m], m++]; m]; nn = 30; t = Table[0, {nn}]; found = 0; sp0 = 4; While[found < nn, sp1 = NextSemiPrime[sp0]; d = sp1 - sp0; If[d <= nn && t[[d]] == 0, t[[d]] = sp0; found++]; sp0 = sp1]; t (* _T. D. Noe_, Oct 02 2012 *)

%Y Cf. A065516, A133478.

%K nonn

%O 1,1

%A _Zak Seidov_, Sep 24 2007

%E Corrected and extended by _T. D. Noe_ and _R. J. Mathar_, Sep 28 2007