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A022931
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Number of e^m between Pi^n and Pi^(n+1).
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0
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1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1
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OFFSET
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0,7
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LINKS
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FORMULA
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a(n) = floor((n + 1) log Pi) - floor(n log Pi). - Alonso del Arte, Dec 20 2018
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EXAMPLE
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Pi^5 = 306.01968478528145326274131... and Pi^6 = 961.389193575304437...; in between them we find e^6 = 403.4287934927351226... and no other powers of e with integer exponents. Hence a(5) = 1.
Pi^6 = 961.389193575304437... and Pi^7 = 3020.2932277767920675142...; in between them we find e^7 = 1096.63315842845859926372... and e^8 = 2980.957987041728274743592... Hence a(6) = 2.
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MAPLE
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Digits:= 30:
log_Pi:= evalf(log(Pi));
a:= n-> floor((n+1)*log_Pi) -floor(n*log_Pi):
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MATHEMATICA
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Table[Floor[(n + 1)Log[Pi]] - Floor[n Log[Pi]], {n, 0, 99}] (* Alonso del Arte, Dec 21 2018 *)
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PROG
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(Scala) val logPi = Math.log(Math.PI); for (n <- 0 to 99) yield (Math.floor(logPi * (n + 1)) - Math.floor(logPi * n)).toInt // Alonso del Arte, Dec 21 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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