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%I #7 Jul 23 2020 13:44:46
%S 1,2,2,4,16,1296,1586874322944
%N a(1) = 1; a(2) = 2; a(n) = [product of digits of a(n-1)]^[product of digits of a(n-2)] for n > 2.
%C The next term -- a(8) -- has 861 digits. Then a(9) equals zero, and any additional terms are indeterminate. - _Harvey P. Dale_, Jul 23 2020
%t a[n_] := (Times @@ IntegerDigits[a[n - 1]])^(Times @@ IntegerDigits[a[n - 2]]); a[1] = 1; a[2] = 2; Table[a[n], {n, 1, 7}]
%t nxt[{a_,b_}]:={b,(Times@@IntegerDigits[b])^Times@@IntegerDigits[a]}; NestList[ nxt,{1,2},7][[All,1]] (* _Harvey P. Dale_, Jul 23 2020 *)
%Y Cf. A070282.
%K base,nonn
%O 1,2
%A _Joseph L. Pe_, May 09 2002
%E Edited by _Robert G. Wilson v_, May 14 2002
%E The next term is too large to include.