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 A006284 Pierce expansion for Euler's constant. (Formerly M1593) 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Jeffrey Shallit, Some predictable Pierce expansions, Fib. Quart., 22 (1984), 332-335. Eric Weisstein's World of Mathematics, Pierce Expansion FORMULA 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 MATHEMATICA 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 *) PROG (PARI) r=1/Euler; for(n=1, 30, r=r/(r-floor(r)); print1(floor(r), ", ")) CROSSREFS Cf. A006275, A006276, A006283. Sequence in context: A030416 A277690 A249342 * A048072 A215246 A230537 Adjacent sequences:  A006281 A006282 A006283 * A006285 A006286 A006287 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 22 09:03 EDT 2020. Contains 337289 sequences. (Running on oeis4.)