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%I M0693 #51 Jan 15 2022 00:01:25
%S 1,1,2,3,5,8,13,21,34,55,91,149,245,404,666,1097,1809,2981,4915,8104,
%T 13360,22027,36316,59875,98716,162755,268338,442414,729417,1202605,
%U 1982760,3269018,5389699,8886111,14650720,24154953,39824785,65659970,108254988,178482301
%N a(n) = ceiling(exp((n-1)/2)).
%C This sequence illustrates the second law of small numbers because it is a coincidence that its first ten terms are the same as the first ten Fibonacci numbers (A000045). - _Alonso del Arte_, Mar 18 2013
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D I. Stewart, L'univers des nombres, pp. 27 Belin-Pour La Science, Paris 2000.
%H Vladimir Pletser, <a href="/A005181/b005181.txt">Table of n, a(n) for n = 0..1000</a>
%H R. K. Guy, <a href="/A005347/a005347.pdf">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
%H R. K. Guy, <a href="http://www.jstor.org/stable/2691503">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20.
%H R. K. Guy and N. J. A. Sloane, <a href="/A005180/a005180.pdf">Correspondence</a>, 1988.
%H I. Stewart, <a href="http://www.whydomath.org/Reading_Room_Material/ian_stewart/9505.html">Fibonacci Forgeries</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StrongLawofSmallNumbers.html">Strong Law of Small Numbers.</a>
%F Limit_{n->oo} a(n+1)/a(n) = sqrt(e) = 1.64872127... = A019774. - _Alois P. Heinz_, Feb 19 2019
%p seq(round(ceil(exp((n-1)/2))), n=0..50); # _Vladimir Pletser_, Sep 15 2013
%t Table[Ceiling[E^((n - 1)/2)], {n, 0, 39}] (* _Alonso del Arte_, Mar 18 2013 *)
%o (Python)
%o import math
%o for n in range(99):
%o print(str(int(math.ceil(math.e**((n-1)*0.5)))), end=', ')
%o # _Alex Ratushnyak_, Mar 18 2013
%Y Cf. A000045, A019774.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, _R. K. Guy_
%E A few more terms from _Alonso del Arte_, Mar 18 2013
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