A072675 -id:A072675 - cp's OEIS frontend

A105501 Numbers n such that 1 is the leading digit of the n-th Fibonacci number in decimal representation.

1, 2, 7, 12, 17, 21, 22, 26, 27, 31, 36, 40, 41, 45, 46, 50, 55, 60, 64, 65, 69, 70, 74, 79, 84, 88, 89, 93, 94, 98, 103, 107, 108, 112, 113, 117, 122, 127, 131, 132, 136, 137, 141, 146, 151, 155, 156, 160, 161, 165, 170, 174, 175, 179, 180, 184, 189, 194, 198, 199

Offset: 1

Reinhard Zumkeller, Apr 11 2005

A008963(a(n)) = 1; A105511(a(n)) = A105511(a(n) - 1) + 1.

			a(10)=31: A008963(31) = A000030(A000045(31)) =
A000030(1346269) = 1.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000030, A000045, A072675, A105502, A105503, A105504, A105505, A105506, A105507, A105508, A105509.

filter:= proc(n) local t;
  t:= combinat:-fibonacci(n);
  t < 2*10^ilog10(t)
end proc:
select(filter, [$1..200]); # Robert Israel, May 02 2018

fQ[n_] := IntegerDigits[Fibonacci[n]][[1]] == 1; Select[Range@200, fQ] (* Robert G. Wilson v, May 02 2018 *)

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

a(n) ~ kn by the equidistribution theorem, where k = log(10)/log(2) = 3.321928.... - Charles R Greathouse IV, Oct 07 2016

A073550 Number of Fibonacci numbers F(k), k <= 10^n, which end in 1.

Original entry on oeis.org

3, 14, 134, 1334, 13334, 133334, 1333334, 13333334, 133333334, 1333333334, 13333333334, 133333333334, 1333333333334, 13333333333334, 133333333333334, 1333333333333334, 13333333333333334, 133333333333333334

Offset: 1

Shyam Sunder Gupta, Aug 15 2002

			a(2) = 14 because there are 14 Fibonacci numbers up to 10^2 which end in 1.

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A072675. Different from A072509.

a(n) = ceiling((10^n-1)/60) + ceiling((10^n-2)/60) + ceiling((10^n-8)/60) + ceiling((10^n-19)/60) + ceiling((10^n-22)/60) + ceiling((10^n-28)/60) + ceiling((10^n-41)/60) + ceiling((10^n-59)/60).

a(n) = ceiling(40/3*10^(n-1)) for n>1. - Benoit Cloitre, Aug 27 2002; [Edited by Felix Fröhlich, Jun 08 2019]

More terms from Vladeta Jovovic, Aug 20 2002

A072509 Number of Fibonacci numbers F(k) <= 10^n which end in 1.

Original entry on oeis.org

2, 2, 3, 3, 4, 5, 6, 6, 6, 7, 7, 7, 8, 10, 11, 11, 11, 13, 13, 14, 14, 15, 15, 15, 15, 17, 18, 19, 19, 20, 21, 22, 22, 22, 23, 23, 23, 23, 26, 27, 27, 27, 29, 29, 30, 30, 31, 31, 31, 31, 32, 34, 35, 35, 36, 37, 38, 38, 38, 39, 39, 39, 39, 42, 42, 43, 43, 45, 45, 46, 46, 47, 47

Offset: 0

Vladeta Jovovic, Aug 23 2002

Note that F(k) ends in 1 if and only if k == 1, 2, 8, 19, 22, 28, 41, or 59 (mod 60). - Robert Israel, May 14 2018

Robert Israel, Table of n, a(n) for n = 0..10000

Different from A073550. Cf. A072353, A072675.

N:= 100: m:= 0:
A:= Array(0..N):
A[0]:= 2:
for i from 0 while m <= N do
  for j in [1, 2, 8, 19, 22, 28, 41, 59] do
    m:= ilog10(combinat:-fibonacci(60*i+j))+1;
    if m > N then break fi;
    A[m..N]:= A[m..N]+1;
od od:
convert(A,list); # Robert Israel, May 14 2018

With[{s = Array[Fibonacci, 350]}, Table[Count[TakeWhile[s, # <= 10^n &], ?(Mod[#, 10] == 1 &)], {n, 0, IntegerLength@ Max@ s}] ] (* _Michael De Vlieger, May 14 2018 *)

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A105501 Numbers n such that 1 is the leading digit of the n-th Fibonacci number in decimal representation.

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A073550 Number of Fibonacci numbers F(k), k <= 10^n, which end in 1.

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A072509 Number of Fibonacci numbers F(k) <= 10^n which end in 1.

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