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A105503 Numbers n such that 3 is the leading digit of the n-th Fibonacci number in decimal representation. 9
4, 9, 14, 28, 33, 38, 52, 57, 71, 76, 81, 95, 100, 105, 119, 124, 138, 143, 148, 162, 167, 172, 181, 186, 191, 205, 210, 215, 229, 234, 239, 248, 253, 258, 272, 277, 282, 296, 301, 306, 315, 320, 325, 339, 344, 349, 363, 368, 382, 387, 392, 406, 411, 416, 430 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A008963(a(n)) = 3; A105513(a(n)) = A105513(a(n) - 1) + 1.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(4) - log(3)) = 8.00392.... - Charles R Greathouse IV, Oct 07 2016

EXAMPLE

a(10)=76: A008963(76) = A000030(A000045(76)) =

A000030(3416454622906707) = 3.

MATHEMATICA

Select[Table[{n, Fibonacci[n]}, {n, 450}], First[IntegerDigits[#[[2]]]]==3&][[All, 1]] (* Harvey P. Dale, Apr 13 2019 *)

PROG

(PARI) is(n)=digits(fibonacci(n))[1]==3 \\ Charles R Greathouse IV, Oct 07 2016

CROSSREFS

Cf. A000030, A000045, A072683, A105501, A105502, A105504, A105505, A105506, A105507, A105508, A105509.

Sequence in context: A073497 A244941 A086192 * A095169 A105703 A055453

Adjacent sequences:  A105500 A105501 A105502 * A105504 A105505 A105506

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Apr 11 2005

EXTENSIONS

Definition clarified by Harvey P. Dale, Apr 13 2019

STATUS

approved

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Last modified May 7 17:19 EDT 2021. Contains 343652 sequences. (Running on oeis4.)