Happy cubes: cubes whose trajectory under iteration of sum of squares of digits map includes 1.

Terms

a(0) =1a(1) =1000a(2) =4096a(3) =12167a(4) =13824a(5) =15625a(6) =74088a(7) =226981a(8) =250047a(9) =300763a(10) =531441a(11) =704969a(12) =778688a(13) =1000000a(14) =1092727a(15) =1481544a(16) =2460375a(17) =2803221a(18) =3176523a(19) =3652264a(20) =4096000a(21) =4251528a(22) =5000211a(23) =6644672a(24) =7645373a(25) =8365427a(26) =8489664a(27) =8869743a(28) =8998912a(29) =11852352