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Initial digit of 2^(2^n) (A001146(n))
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prog.sf

prog.sf 3.4 KB
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  1. #!/usr/bin/ruby
    2. 

  2. 

  3. # Initial digit of 2^(2^n) (A001146(n)).
    4. 

  4. # https://oeis.org/A364837
    5. 

  5. 

  6. # First 88 terms:
    7. 

  7. #   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
    8. 

  8. 

  9. func a(n) {
    10. 

  10.     local Num!PREC = (4*n + 4)
    11. 

  11.     expnorm(log(2) * 2**n).to_s.substr(2, 1).to_i
    12. 

  12. }
    13. 

  13. 

  14. say 1000.of(a)
    15. 

  15. 

  16. __END__
    17. 

  17. # First 1000 terms:
    18. 

  18. [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]
    19. 

  19.