OFFSET
0,3
COMMENTS
This sequence illustrates the second law of small numbers because it is a coincidence that its first ten terms are the same as the Fibonacci numbers F(1), ..., F(10) (A000045). - Alonso del Arte, Mar 18 2013 [Clarified by Eric W. Weisstein, Oct 13 2026]
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
I. Stewart, L'univers des nombres, pp. 27 Belin-Pour La Science, Paris 2000.
LINKS
Vladimir Pletser, Table of n, a(n) for n = 0..1000
R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20.
R. K. Guy and N. J. A. Sloane, Correspondence, 1988.
I. Stewart, Fibonacci Forgeries
Eric Weisstein's World of Mathematics, Fibonacci Number.
Eric Weisstein's World of Mathematics, Strong Law of Small Numbers.
FORMULA
Limit_{n->oo} a(n+1)/a(n) = sqrt(e) = 1.64872127... = A019774. - Alois P. Heinz, Feb 19 2019
MAPLE
seq(round(ceil(exp((n-1)/2))), n=0..50); # Vladimir Pletser, Sep 15 2013
MATHEMATICA
Table[Ceiling[E^((n - 1)/2)], {n, 0, 39}] (* Alonso del Arte, Mar 18 2013 *)
PROG
(Python)
import math
for n in range(99):
print(str(int(math.ceil(math.e**((n-1)*0.5)))), end=', ')
# Alex Ratushnyak, Mar 18 2013
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
EXTENSIONS
A few more terms from Alonso del Arte, Mar 18 2013
STATUS
approved
