cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

A072351 Smallest n-digit Fibonacci number.

Original entry on oeis.org

1, 13, 144, 1597, 10946, 121393, 1346269, 14930352, 102334155, 1134903170, 12586269025, 139583862445, 1548008755920, 10610209857723, 117669030460994, 1304969544928657, 14472334024676221, 160500643816367088, 1100087778366101931, 12200160415121876738
Offset: 1

Views

Author

Shyam Sunder Gupta, Jul 17 2002

Keywords

Examples

			a(3)=144, as 144 is smallest 3-digit Fibonacci number.

Links

Crossrefs

Cf. A072352, A105710, A105712, A105713, A105714, A105715, A105716, A105717, A105718, A105719.

Programs

  • Maple
    F:= proc(n) option remember; local f;
      f:= `if`(n=1, [1$2], F(n-1));
      do f:= [f[2], f[1]+f[2]];
         if length(f[1]) `if`(n=1, 1, F(n-1)[2]):
seq(a(n), n=1..25);  # Alois P. Heinz, Mar 10 2016
  • Mathematica
    a[n_] := Fibonacci[Ceiling[k /. FindRoot[Log[10, Fibonacci[k]] == n-1, {k, 1}]]]; Array[a, 20] (* Jean-François Alcover, Jan 18 2017 *)
With[{fbs=Fibonacci[Range[100]]},Table[SelectFirst[fbs,IntegerLength[#]==n&],{n,20}]] (* Harvey P. Dale, Dec 13 2024 *)
  • PARI
    A072351(n,phi=(sqrt(5)+1)/2)=round(phi^ceil((n*log(10)+log(5)/2)/log(phi))/sqrt(5)) \\  Franklin T. Adams-Watters, May 27 2011
  • Python
    def A072351_list(n):
    list = [1]
    x, y = 1, 1
    while len(list) < n:
        if len(str(x)) < len(str(y)):
            list.append(y)
        x, y = y, x + y
    return list
print(A072351_list(20)) # M. Eren Kesim, Jun 28 2021

Formula

A072351(n) = floor(1/2 + phi^ceiling((n*log(10) + (1/2)*log(5))/log(phi))/sqrt(5)). - Franklin T. Adams-Watters, May 27 2011

A105717 Smallest Fibonacci number that has 7 in the n-th position of the decimal representation.

Original entry on oeis.org

377, 377, 6765, 17711, 75025, 5702887, 267914296, 2971215073, 701408733, 7778742049, 27777890035288, 27777890035288, 17167680177565, 72723460248141, 51680708854858323072, 37889062373143906, 679891637638612258
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

a(n) = A000045(A105707(n)).
The n-th position is counted from the right. - Harvey P. Dale, Jul 22 2024

Examples

			n=3: A105700(3)=22, a(3)=A000045(22)=17711->1[7]711;
n=4: A105700(4)=25, a(4)=A000045(25)=75025->[7]5025.

Links

Crossrefs

Cf. A105711, A072351, A105712, A105713, A105714, A105715, A105716, A105718, A105719.

Programs

  • Maple
    N:= 100: # for a(0)..a(N)
F[0]:= 0: F[1]:= 1:
W:= Array(0..N):
count:= 0:
for m from 2 while count < N do
  F[m]:= F[m-1]+F[m-2];
  L:= convert(F[m],base,10);
  M:= select(t -> L[t+1]=7 and W[t]=0, [$0..min(N,nops(L)-1)]);
  count:= count + nops(M);
  W[M]:= F[m]
od:
convert(W,list); # Robert Israel, Jun 01 2020
  • Mathematica
    With[{fibs=Fibonacci[Range[150]]},Table[SelectFirst[fibs,NumberDigit[#,n-1]==7&],{n,20}]] (* Harvey P. Dale, Jul 22 2024 *)

Extensions

Definition corrected by Robert Israel, Jun 01 2020

A105706 Smallest m such that 6 is at the n-th position of the decimal representation of the m-th Fibonacci number.

Original entry on oeis.org

21, 20, 15, 20, 50, 79, 46, 39, 65, 54, 57, 64, 63, 90, 85, 106, 82, 87, 106, 110, 108, 106, 117, 121, 124, 131, 130, 162, 149, 180, 149, 154, 167, 176, 179, 173, 212, 193, 191, 197, 197, 215, 213, 221, 216, 221, 232, 239, 248, 240, 252, 264, 286, 259, 264, 277
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

A105716(n) = A000045(a(n)).

Examples

			n=3: a(3)=20, A000045(20)=A105710(3)=6765->[6]765;
n=4: a(4)=50,
A000045(50)=A105710(4)=12586269025->125862[6]9025.

Links

Crossrefs

Cf. A105701, A072354, A105702, A105703, A105704, A105705, A105707, A105708, A105709.

A105712 Smallest m such that 2 is at the n-th position of the decimal representation of the m-th Fibonacci number.

Original entry on oeis.org

2, 21, 233, 2584, 28657, 9227465, 2178309, 24157817, 267914296, 2971215073, 20365011074, 225851433717, 2504730781961, 27777890035288, 19740274219868223167, 2111485077978050, 23416728348467685
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

a(n) = A000045(A105702(n)).

Examples

			n=3: A105700(3)=18, a(3)=A000045(18)=2584->[2]584;
n=4: A105700(4)=23, a(4)=A000045(23)=28657->[2]8657.

Links

Crossrefs

Cf. A105711, A072351, A105713, A105714, A105715, A105716, A105717, A105718, A105719.

A105713 Smallest m such that 3 is at the n-th position of the decimal representation of the m-th Fibonacci number.

Original entry on oeis.org

3, 34, 377, 1134903170, 832040, 317811, 3524578, 39088169, 20365011074, 53316291173, 32951280099, 365435296162, 7540113804746346429, 31940434634990099905, 308061521170129, 3416454622906707
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

a(n) = A000045(A105703(n)).

Examples

			n=3: A105700(3)=45,
a(3)=A000045(45)=1134903170->113490[3]170;
n=4: A105700(4)=30, a(4)=A000045(30)=832040->8[3]2040.

Links

Crossrefs

Cf. A105711, A072351, A105712, A105714, A105715, A105716, A105717, A105718, A105719.

A105714 Smallest m such that 4 is at the n-th position of the decimal representation of the m-th Fibonacci number.

Original entry on oeis.org

34, 144, 196418, 4181, 46368, 433494437, 14930352, 1304969544928657, 433494437, 4807526976, 1548008755920, 498454011879264, 4052739537881, 44945570212853, 498454011879264, 14472334024676221, 7540113804746346429
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

a(n) = A000045(A105704(n)).

Examples

			n=3: A105700(3)=19, a(3)=A000045(19)=4181->[4]181;
n=4: A105700(4)=24, a(4)=A000045(24)=46368->[4]6368.

Links

Crossrefs

Cf. A105711, A072351, A105712, A105713, A105715, A105716, A105717, A105718, A105719.

A105715 Smallest m such that 5 is at the n-th position of the decimal representation of the m-th Fibonacci number.

Original entry on oeis.org

5, 55, 1597, 75025, 24157817, 514229, 5702887, 32951280099, 12586269025, 225851433717, 53316291173, 591286729879, 61305790721611591, 135301852344706746049, 5527939700884757, 5527939700884757
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

a(n) = A000045(A105705(n)).

Examples

			n=3: A105700(3)=25, a(3)=A000045(25)=75025->7[5]025;
n=4: A105700(4)=37, a(4)=A000045(37)=24157817->241[5]7817.

Links

Crossrefs

Cf. A105711, A072351, A105712, A105713, A105714, A105716, A105717, A105718, A105719.

A105718 Smallest Fibonacci number such that 8 is at the n-th position (from the right) of its decimal representation.

Original entry on oeis.org

8, 89, 317811, 28657, 39088169, 832040, 7778742049, 12586269025, 1836311903, 1548008755920, 86267571272, 99194853094755497, 308061521170129, 37889062373143906, 806515533049393, 8944394323791464, 2880067194370816120
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

a(n) = A000045(A105708(n)).

Examples

			n=3: A105700(3)=23, a(3)=A000045(23)=28657->2[8]657;
n=4: A105700(4)=38, a(4)=A000045(38)=39088169->390[8]8169.

Links

Crossrefs

Cf. A105711, A072351, A105712, A105713, A105714, A105715, A105716, A105717, A105719.

Extensions

Definition corrected by Robert Israel, Apr 25 2021

A105719 Smallest m such that 9 is at the n-th position of the decimal representation of the m-th Fibonacci number.

Original entry on oeis.org

89, 1597, 987, 12586269025, 196418, 14930352, 9227465, 27777890035288, 2971215073, 139583862445, 591286729879, 956722026041, 37889062373143906, 190392490709135, 8944394323791464, 99194853094755497, 99194853094755497
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

a(n) = A000045(A105709(n)).

Examples

			n=3: A105700(3)=50,
a(3)=A000045(50)=12586269025->1258626[9]025;
n=4: A105700(4)=27, a(4)=A000045(27)=196418->1[9]6418.

Links

Crossrefs

Cf. A105711, A072351, A105712, A105713, A105714, A105715, A105716, A105717, A105718.

A105711 Smallest m such that 0 is at the n-th position of the decimal representation of the m-th Fibonacci number.

Original entry on oeis.org

0, 2178309, 75025, 10946, 5702887, 39088169, 2504730781961, 102334155, 1548008755920, 20365011074, 2504730781961, 4052739537881, 10610209857723, 308061521170129, 1100087778366101931, 160500643816367088
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

a(n) = A000045(A105701(n)).

Examples

			n=3: A105701(3)=21, a(3)=A000045(21)=10946->1[0]946;
n=4: A105701(4)=34, a(4)=A000045(34)=5702887->57[0]2887.

Links

Crossrefs

Cf. A072351, A105712, A105713, A105714, A105715, A105716, A105717, A105718, A105719.
Showing 1-10 of 10 results.

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