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%I #2 Mar 30 2012 17:34:20
%S 1,3,7,13,33,47,132,458,777,853,3845,4395,4783,4983,6038,6487,6719,
%T 6957,11707,12030,12688,13025,13365,13709,14057,14409,15861,17789,
%U 18598,19008,19845,20272,20702,21135,21570,22010,22458,23378,23850,24326
%N Terms in A112039 that are divisible by 3, divided by 3.
%C These integers also form a kind of prime with the a[2*n]/3 as a discriminant. dd = Flatten[Table[If[IntegerQ[a[2*n]/3] == True, Prime[n], {}], {n, 1, 200}]] 2, 3, 5, 7, 13, 17, 31, 67, 89, 97, 227, 239, 251, 257, 281, 293, 307, 311, 419, 421, 433, 439, 443, 449, 457, 461, 487, 521, 541, 547, 563, 569, 571, 577, 587, 593, 599, 607, 613, 617, 641, 643, 647, 653, 673, 743, 751, 769, 853, 857, 859, 863, 877, 881, 911, 919, 929, 947, 953, 967, 977, 983, 991, 997, 1009, 1031, 1039, 1063
%F a(0)=1/2 a(n) = a(n-1) + Prime[n]/2 if a[2*n]/3 is an Integer then aout=a[2*n]/3
%t a[0] = 1/2; a[n_] := a[n] = a[n - 1] + Prime[n]/2 cc = Flatten[Table[If[IntegerQ[a[2*n]/3] == True, a[2*n]/3, {}], {n, 1, 200}]]
%K nonn
%O 1,2
%A _Roger L. Bagula_, Nov 28 2005