a(n) = smallest k such that k! ends in 2^n, not counting the trailing zeros.

Terms

a(0) =0a(1) =2a(2) =4a(3) =9a(4) =12a(5) =8a(6) =20a(7) =33a(8) =159a(9) =43a(10) =49a(11) =348a(12) =60a(13) =91a(14) =8134a(15) =1964a(16) =1392a(17) =735a(18) =34060a(19) =9030a(20) =14052a(21) =39306a(22) =16906a(23) =29338a(24) =53711a(25) =356449a(26) =88137a(27) =543041a(28) =1435398a(29) =1000154