The On-Line Encyclopedia of Integer Sequences (OEIS)

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A105053

Least number k such that (1+1/k)^k yields n digits of e (A001113).
(history; published version)

#4 by Russ Cox at Fri Mar 30 17:31:12 EDT 2012

AUTHOR

_Robert G. Wilson v (rgwv(AT)rgwv.com), _, Apr 02 2005

Discussion

Fri Mar 30

17:31

OEIS Server: https://oeis.org/edit/global/156

#3 by Charles R Greathouse IV at Sun Nov 14 22:19:23 EST 2010

STATUS

proposed

approved

#2 by Charles R Greathouse IV at Sun Nov 14 22:19:21 EST 2010

KEYWORD

nonn,base,new

STATUS

approved

proposed

#1 by N. J. A. Sloane at Sat Apr 09 03:00:00 EDT 2005

NAME

Least number k such that (1+1/k)^k yields n digits of e (A001113).

DATA

1, 74, 164, 4822, 16609, 743325, 1640565, 45332594

OFFSET

1,2

EXAMPLE

a(1) = 1 because (1+1/1)^1= 2 which equals e in the units place.

a(2) = 74 because (1+1/73)^73 = 2.69989... but (1+1/74)^74 = 2.700139...; thus 74 is the least number which will give e to 2 place accuracy, namely 2.7.

MATHEMATICA

f[0] = 0; f[n_] := f[n] = Block[{k = f[n - 1] + 1, d = FromDigits[{Take[ RealDigits[E, 10, 111][[1]], n], 1}]}, While[(1 + 1/k)^k < d, k++ ]; k]; Table[ f[n], {n, 6}]

CROSSREFS

Cf. A001113.

KEYWORD

nonn,new

AUTHOR

Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 02 2005

STATUS

approved