A060384 - OEIS

A060384

Number of decimal digits in n-th Fibonacci number.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18

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OFFSET

0,8

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..10000

Andreas Guthmann, Wieviele k-stellige Fibonaccizahlen gibt es?, Archiv der Mathematik, 59(4):334-340, October 1992.

FORMULA

a(n) = floor(n*log(phi)/log(10)) +0 or +1 where phi is the golden ratio. - Benoit Cloitre, Oct 29 2002. [Corrected by Hans J. H. Tuenter, Jul 07 2025].

a(n) = floor(n*log_10(phi) - log_10(5)/2) + 1 for n >= 2, where phi is (1+sqrt(5))/2. - Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007

a(n) = A055642(A000045(n)). - Reinhard Zumkeller, Mar 09 2013

MAPLE

with(combinat): a:=n->nops(convert(fibonacci(n), base, 10)): 1, seq(a(n), n=1..100); # Emeric Deutsch, May 19 2007

MATHEMATICA

Table[IntegerLength@ Fibonacci@ n, {n, 0, 84}] /. 0 -> 1 (* or *)

Table[Floor[n Log10@ GoldenRatio - Log10@ 5/2] + 1, {n, 0, 84}] /. 0 -> 1 (* Michael De Vlieger, Jul 04 2016 *)

PROG

(PARI) print1("1, 1, "); gold=(1+sqrt(5))/2; for(n=2, 100, print1(floor((n*log(gold)-log(5)/2)/log(10))+1", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007

(PARI) a(n) = #Str(fibonacci(n)); \\ Michel Marcus, Jul 04 2016

(Haskell)

a060384 = a055642 . a000045 -- Reinhard Zumkeller, Mar 09 2013

CROSSREFS

Cf. A000045, A022307, A001605, A060319, A060320, A051694, A050815.

Cf. A261585.

Sequence in context: A105511 A187183 A027868 * A105564 A241766 A351646

Adjacent sequences: A060381 A060382 A060383 * A060385 A060386 A060387

KEYWORD

base,nonn

AUTHOR

Labos Elemer, Apr 03 2001

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007

STATUS

approved