a(2)=3 because successive iterations give 2 -> 4 -> 7 -> 13 -> 16 -> 13 etc.
CROSSREFS
Cf. A004159 for sum of digits of square, A056528 for two iterations, A056020 where iteration settles to 1, A056020 where iteration settles to 9, A056527 where iteration settles to 13 and 16.