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A105505 Numbers n such that 5 is the leading digit of the n-th Fibonacci number in decimal representation. 9
5, 10, 29, 34, 53, 58, 77, 96, 101, 120, 125, 139, 144, 163, 168, 187, 192, 206, 211, 230, 235, 254, 273, 278, 297, 302, 321, 340, 345, 364, 369, 388, 407, 412, 431, 436, 455, 474, 479, 498, 503, 522, 541, 546, 565, 570, 584, 589, 608, 613, 632, 637, 651, 656 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A008963(a(n)) = 5; A105515(a(n)) = A105515(a(n) - 1) + 1.

LINKS

Table of n, a(n) for n=1..54.

FORMULA

a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(6) - log(5)) = 12.629253.... - Charles R Greathouse IV, Oct 07 2016

EXAMPLE

a(10)=120: A008963(120) = A000030(A000045(120)) =

A000030(5358359254990966640871840) = 5.

MATHEMATICA

Select[Range[700], First[IntegerDigits[Fibonacci[#]]]==5&] (* Harvey P. Dale, Jul 31 2018 *)

PROG

(PARI) is(n)=digits(fibonacci(n))[1]==5 \\ Charles R Greathouse IV, Oct 07 2016

CROSSREFS

Cf. A000030, A000045, A072703, A105501, A105502, A105503, A105504, A105506, A105507, A105508, A105509.

Sequence in context: A240515 A105862 A093029 * A005514 A069921 A053818

Adjacent sequences:  A105502 A105503 A105504 * A105506 A105507 A105508

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Apr 11 2005

STATUS

approved

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)