a(n) = T(p(n)) - p(T(n)) = Commutator[triangular numbers, primes] at n.

Terms

a(0) =1a(1) =1a(2) =2a(3) =-1a(4) =19a(5) =18a(6) =46a(7) =39a(8) =79a(9) =178a(10) =179a(11) =306a(12) =394a(13) =375a(14) =469a(15) =662a(16) =887a(17) =872a(18) =1127a(19) =1265a(20) =1248a(21) =1553a(22) =1703a(23) =2018a(24) =2600a(25) =2780a(26) =2763a(27) =2987a(28) =2958a(29) =3134