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prog.sf
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#!/usr/bin/ruby
# Initial digit of 2^(2^n) (A001146(n)).
# https://oeis.org/A364837
# First 88 terms:
# 2, 4, 1, 2, 6, 4, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 2, 4, 1, 2, 6, 4, 2, 4, 1, 3, 1, 1, 1, 2, 4, 1, 3, 9, 9, 8, 7, 5, 2, 8, 8, 6, 4, 1, 3, 9, 9, 9, 9, 9, 8, 7, 5, 2, 8, 7, 6, 3, 1, 2, 5, 3, 1, 1, 1, 3, 1, 1, 3, 9, 8, 7, 5, 3, 1, 1, 1, 3, 1, 2, 4, 2, 5, 2, 6, 4, 1, 2
func a(n) {
local Num!PREC = (4*n + 4)
expnorm(log(2) * 2**n).to_s.substr(2, 1).to_i
}
say 1000.of(a)
__END__
# First 1000 terms:
[2, 4, 1, 2, 6, 4, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 2, 4, 1, 2, 6, 4, 2, 4, 1, 3, 1, 1, 1, 2, 4, 1, 3, 9, 9, 8, 7, 5, 2, 8, 8, 6, 4, 1, 3, 9, 9, 9, 9, 9, 8, 7, 5, 2, 8, 7, 6, 3, 1, 2, 5, 3, 1, 1, 1, 3, 1, 1, 3, 9, 8, 7, 5, 3, 1, 1, 1, 3, 1, 2, 4, 2, 5, 2, 6, 4, 1, 2, 6, 4, 2, 4, 2, 5, 3, 1, 1, 1, 1, 1, 2, 5, 2, 7, 5, 3, 9, 8, 7, 6, 3, 1, 1, 3, 1, 1, 3, 1, 1, 2, 5, 2, 8, 7, 5, 3, 1, 1, 1, 1, 2, 4, 1, 2, 6, 4, 2, 4, 2, 5, 2, 6, 4, 1, 3, 1, 2, 5, 3, 1, 1, 1, 2, 5, 3, 1, 1, 2, 4, 2, 4, 1, 3, 1, 1, 1, 3, 9, 8, 6, 4, 1, 3, 1, 1, 3, 9, 8, 7, 6, 4, 1, 2, 6, 4, 1, 3, 1, 1, 3, 1, 2, 5, 3, 1, 1, 2, 4, 1, 3, 1, 2, 5, 2, 8, 7, 6, 4, 1, 2, 7, 5, 2, 8, 7, 6, 3, 1, 2, 4, 1, 2, 6, 4, 2, 5, 2, 7, 5, 3, 9, 8, 7, 6, 3, 1, 2, 5, 3, 1, 1, 2, 6, 3, 1, 1, 2, 8, 7, 6, 3, 1, 2, 4, 2, 6, 3, 1, 2, 4, 1, 3, 1, 1, 1, 2, 6, 4, 2, 4, 1, 3, 1, 1, 2, 5, 2, 6, 4, 2, 5, 3, 1, 1, 1, 1, 1, 2, 6, 3, 1, 1, 3, 1, 1, 2, 6, 4, 1, 3, 9, 9, 9, 8, 6, 4, 2, 4, 2, 5, 2, 8, 8, 6, 4, 1, 3, 1, 1, 1, 2, 4, 1, 2, 8, 7, 6, 3, 1, 2, 5, 2, 7, 6, 3, 1, 2, 5, 2, 8, 7, 5, 3, 1, 1, 2, 7, 6, 3, 1, 2, 6, 4, 1, 2, 6, 4, 1, 3, 1, 1, 2, 7, 5, 3, 1, 1, 2, 7, 5, 3, 9, 8, 6, 4, 1, 3, 1, 1, 1, 3, 1, 2, 4, 1, 3, 1, 1, 3, 1, 1, 2, 4, 1, 3, 1, 1, 2, 7, 6, 4, 1, 2, 6, 4, 1, 3, 1, 1, 3, 1, 2, 4, 2, 5, 2, 7, 4, 2, 5, 3, 1, 1, 2, 5, 3, 1, 1, 2, 5, 2, 7, 6, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 2, 8, 7, 6, 3, 1, 2, 4, 2, 5, 3, 1, 1, 2, 5, 2, 6, 4, 2, 4, 1, 3, 1, 2, 4, 1, 3, 9, 9, 9, 9, 8, 6, 4, 2, 4, 1, 3, 1, 1, 3, 1, 2, 4, 2, 4, 2, 4, 1, 3, 1, 2, 5, 2, 6, 4, 1, 3, 1, 2, 5, 2, 6, 3, 1, 2, 5, 3, 1, 1, 2, 5, 3, 9, 9, 8, 7, 5, 3, 1, 1, 1, 1, 2, 7, 5, 3, 9, 9, 8, 7, 5, 3, 9, 8, 7, 5, 2, 7, 5, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 4, 2, 4, 2, 4, 2, 4, 2, 5, 2, 7, 6, 3, 1, 2, 5, 2, 8, 7, 6, 3, 1, 2, 4, 1, 2, 8, 6, 4, 1, 2, 8, 7, 6, 3, 1, 1, 2, 8, 6, 4, 1, 3, 1, 1, 2, 6, 3, 1, 1, 3, 1, 1, 1, 2, 5, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 5, 3, 1, 1, 1, 1, 1, 1, 2, 5, 2, 7, 6, 3, 1, 2, 5, 2, 8, 6, 4, 1, 3, 1, 2, 4, 1, 2, 6, 4, 2, 5, 3, 1, 1, 1, 2, 4, 1, 2, 7, 6, 3, 1, 2, 5, 3, 9, 9, 9, 8, 7, 5, 2, 8, 7, 6, 4, 1, 2, 7, 5, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 5, 3, 9, 8, 6, 4, 2, 4, 1, 2, 8, 6, 4, 2, 5, 2, 7, 6, 3, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 2, 4, 2, 4, 1, 2, 7, 4, 2, 5, 3, 1, 1, 2, 4, 2, 4, 2, 6, 3, 1, 1, 3, 1, 2, 5, 2, 7, 5, 2, 6, 4, 1, 2, 8, 7, 5, 2, 7, 5, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 2, 6, 4, 2, 5, 3, 9, 9, 9, 8, 6, 4, 2, 4, 1, 3, 1, 2, 5, 2, 6, 4, 1, 3, 9, 8, 6, 4, 2, 4, 2, 5, 3, 1, 1, 2, 4, 2, 4, 2, 4, 1, 3, 9, 8, 6, 4, 2, 5, 3, 1, 1, 1, 1, 1, 1, 2, 4, 2, 5, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 6, 4, 1, 2, 8, 7, 5, 3, 1, 1, 2, 4, 2, 6, 3, 1, 2, 4, 1, 3, 1, 1, 1, 1, 2, 6, 4, 2, 4, 2, 5, 2, 7, 5, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 5, 2, 6, 4, 2, 4, 1, 3, 1, 1, 2, 7, 5, 2, 6, 4, 1, 3, 9, 8, 7, 5, 2, 7, 5, 3, 1, 1, 1, 1, 1, 2, 4, 1, 2, 8, 8, 6, 4, 1, 3, 9, 8, 6, 4, 1, 3, 1, 2, 6, 3, 1, 1, 3, 1, 1, 3, 9, 9, 8, 7, 5, 3, 9, 8, 7, 5, 3, 9, 8, 7, 5, 2, 8, 6, 4, 2, 4, 1, 3, 1, 1, 2, 5, 3, 1, 1, 2, 5, 2, 8, 7, 5, 3, 9, 8, 7, 6, 3, 1, 1, 3, 1, 1]