Tetrahedral numbers k*(k+1)*(k+2)/6 such that exactly two of k, k+1, and k+2 are prime.

Terms

a(0) =1a(1) =4a(2) =10a(3) =35a(4) =286a(5) =969a(6) =4495a(7) =12341a(8) =35990a(9) =62196a(10) =176851a(11) =209934a(12) =437989a(13) =562475a(14) =971970a(15) =1179616a(16) =1293699a(17) =1975354a(18) =2303960a(19) =3280455a(20) =3737581a(21) =5061836a(22) =7023974a(23) =12347930a(24) =13436856a(25) =16435111a(26) =23706021a(27) =30865405a(28) =35999900a(29) =39338069