A005181 a(n) = ceiling(exp((n-1)/2)). (Formerly M0693)

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 91, 149, 245, 404, 666, 1097, 1809, 2981, 4915, 8104, 13360, 22027, 36316, 59875, 98716, 162755, 268338, 442414, 729417, 1202605, 1982760, 3269018, 5389699, 8886111, 14650720, 24154953, 39824785, 65659970, 108254988, 178482301

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 first ten Fibonacci numbers (A000045). - Alonso del Arte, Mar 18 2013

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

Cf. A000045, A019774.

Sequence in context: A077371 A077372 A147659 * A177376 A120659 A042581

Adjacent sequences: A005178 A005179 A005180 * A005182 A005183 A005184

Keyword

nonn

Author

N. J. A. Sloane, R. K. Guy

Extensions

A few more terms from Alonso del Arte, Mar 18 2013

Status

approved