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A006284
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Pierce expansion for Euler's constant.
(Formerly M1593)
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3
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1, 2, 6, 13, 21, 24, 225, 615, 17450, 23228, 57774, 221361, 522377, 793040, 1706305, 8664354, 19037086, 51965160, 56870701, 124645388, 784244500, 792809072, 3675221276, 42108268014, 53633289500, 56827261536, 67080647365
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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If u(0) = exp(1/m), where m is an integer >=1, and u(n+1) = u(n)/frac(u(n)) then floor(u(n)) = m*n. Let u(0)=1/gamma and u(n+1) = u(n)/frac(u(n)) where frac(x) is the fractional part of x, then a(n) = floor(u(n)) - Benoit Cloitre, Mar 09 2004
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MATHEMATICA
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PierceExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@ NestList[{Floor[1/Expand[1 - #[[1]] #[[2]]]], Expand[1 - #[[1]] #[[2]]]} &, {Floor[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; PierceExp[N[EulerGamma, 7!], 25] (* G. C. Greubel, Nov 14 2016 *)
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PROG
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(PARI) r=1/Euler; for(n=1, 30, r=r/(r-floor(r)); print1(floor(r), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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