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 11 results. Next

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

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.

A105716 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

10946, 6765, 610, 6765, 12586269025, 14472334024676221, 1836311903, 63245986, 17167680177565, 86267571272, 365435296162, 10610209857723, 6557470319842, 2880067194370816120, 259695496911122585, 6356306993006846248183
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

a(n) = A000045(A105706(n)).

Examples

			n=3: A105700(3)=20, a(3)=A000045(20)=6765->[6]765;
n=4: A105700(4)=50,
a(4)=A000045(50)=12586269025->125862[6]9025.

Links

Crossrefs

Cf. A105711, A072351, A105712, A105713, A105714, A105715, 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.

A072353 a(n) is the index of the largest Fibonacci number containing n digits.

Original entry on oeis.org

6, 11, 16, 20, 25, 30, 35, 39, 44, 49, 54, 59, 63, 68, 73, 78, 83, 87, 92, 97, 102, 106, 111, 116, 121, 126, 130, 135, 140, 145, 150, 154, 159, 164, 169, 173, 178, 183, 188, 193, 197, 202, 207, 212, 216, 221, 226, 231, 236, 240, 245, 250, 255, 260, 264, 269, 274
Offset: 1

Views

Author

Shyam Sunder Gupta, Jul 17 2002

Keywords

Comments

Partial sums of A050815: a(n) = Sum_{k=1..n} A050815(k). - Reinhard Zumkeller, Apr 14 2005
Equivalently, a(n) is the number of Fibonacci numbers < 10^n including F(0) = 0 and F(1) = F(2) = 1 once. - Derek Orr, Jun 01 2014

Examples

			a(3)=16, as the 16th Fibonacci number is the largest Fibonacci number with 3 digits.

Links

Crossrefs

Cf. A072351, A072352, A105564, A105566, A097348, A050815, A060384, A000045.

Programs

  • Mathematica
    With[{fibs=Fibonacci[Range[300]]},Flatten[Position[fibs,#]&/@ Table[ Max[ Select[fibs,IntegerLength[#]==n&]],{n,60}]]] (* Harvey P. Dale, Nov 09 2011 *)
  • Python
    def A072353_list(n):
    list = []
    x, y, index = 1, 1, 1
    while len(list) < n:
        if len(str(x)) < len(str(y)):
            list.append(index)
        x, y = y, x + y
        index += 1
    return list
print(A072353_list(57)) # M. Eren Kesim, Jul 19 2021

Formula

Limit_{n->oo} a(n)/n = 1/log_10((1+sqrt(5))/2) = 1/A097348 = 4.784... . - Reinhard Zumkeller, Apr 14 2005.
a(n) = floor(n*log(10)/log(phi)+log(5)/(2*log(phi))), where phi=(1+sqrt(5))/2, the golden ratio. - Hans J. H. Tuenter, Jul 08 2025

Extensions

More terms from Reinhard Zumkeller, Apr 14 2005
Name edited by Michel Marcus, Jul 19 2021
Showing 1-10 of 11 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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