A112040 Terms in A112039 that are divisible by 3, divided by 3.

1, 3, 7, 13, 33, 47, 132, 458, 777, 853, 3845, 4395, 4783, 4983, 6038, 6487, 6719, 6957, 11707, 12030, 12688, 13025, 13365, 13709, 14057, 14409, 15861, 17789, 18598, 19008, 19845, 20272, 20702, 21135, 21570, 22010, 22458, 23378, 23850, 24326

Offset: 1

Author

Roger L. Bagula, Nov 28 2005

Keywords

• nonn

Comments

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

Programs

Mathematica

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}]]

Formula

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