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.

A072354 a(n)-th Fibonacci number is the smallest Fibonacci number containing n digits.

Original entry on oeis.org

1, 7, 12, 17, 21, 26, 31, 36, 40, 45, 50, 55, 60, 64, 69, 74, 79, 84, 88, 93, 98, 103, 107, 112, 117, 122, 127, 131, 136, 141, 146, 151, 155, 160, 165, 170, 174, 179, 184, 189, 194, 198, 203, 208, 213, 217, 222, 227, 232, 237
Offset: 1

Views

Author

Shyam Sunder Gupta, Jul 18 2002

Keywords

Examples

			a(3) = 12 as the 12th Fibonacci number is the smallest Fibonacci number with 3 digits.

Links

Crossrefs

Cf. A001622, A105700, A105702, A105703, A105704, A105705, A105706, A105707, A105708, A105709.

Programs

  • Mathematica
    Flatten[Table[Position[IntegerLength[Fibonacci[Range[250]]],n,{1},1],{n,50}]] (* Harvey P. Dale, Dec 22 2015 *)
  • PARI
    a(n)={my(k=1); while(logint(fibonacci(k),10)Harry J. Smith, Nov 29 2008

Formula

For n>1, a(n) = A072353(n-1) + 1. - Michel Marcus, Jun 01 2014
For n>1, a(n) = ceiling(n*log(10)/log(phi)-log(20)/(2*log(phi))), where phi=(1+sqrt(5))/2, the golden ratio. - Hans J. H. Tuenter, Jul 13 2025

A105707 Smallest m such that 7 is at the n-th position of the decimal representation of the m-th Fibonacci number.

Original entry on oeis.org

14, 14, 20, 22, 25, 34, 42, 47, 44, 49, 66, 66, 65, 68, 96, 81, 87, 89, 92, 101, 116, 145, 111, 116, 129, 153, 132, 135, 167, 159, 159, 156, 159, 168, 175, 176, 178, 183, 217, 198, 199, 202, 221, 223, 249, 223, 226, 235, 266, 243, 245, 250, 258, 265, 266, 269
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

Positions start with the 0th position on the right. - Robert Israel, Jun 01 2020

Examples

			n=3: a(3)=22, A000045(22) = A105710(3) = 17711 -> 1[7]711;
n=4: a(4)=25, A000045(25) = A105710(4) = 75025 -> [7]5025.

Links

Crossrefs

Cf. A105701, A072354, A105702, A105703, A105704, A105705, A105706, A105708, A105709.

Programs

  • Maple
    N:= 100: # for a(0) to a(N)
F[0]:= 0: F[1]:= 1:
V:= Array(0..N):
count:= 0:
for m from 2 while count < N+1 do
  F[m]:= F[m-1]+F[m-2];
  L:= convert(F[m],base,10);
  M:= select(t -> L[t+1]=7 and V[t]=0, [$0..min(N,nops(L)-1)]);
  count:= count + nops(M);
  V[M]:= m;
od:
convert(V,list); # Robert Israel, Jun 01 2020

Formula

A000045(a(n)) = A105717(n).

A105708 Smallest m such that 8 is at the n-th position of the decimal representation of the m-th Fibonacci number.

Original entry on oeis.org

6, 11, 28, 23, 38, 30, 49, 50, 46, 60, 54, 83, 71, 81, 73, 78, 90, 90, 99, 97, 126, 114, 113, 135, 121, 146, 136, 145, 140, 145, 154, 157, 170, 164, 178, 186, 180, 190, 188, 203, 200, 211, 207, 215, 221, 246, 235, 231, 242, 249, 247, 272, 255, 269, 267, 290, 274
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

A105718(n) = A000045(a(n)).

Examples

			n=3: a(3)=23, A000045(23)=A105718(3)=28657->2[8]657;
n=4: a(4)=38, A000045(38)=A105718(4)=39088169->390[8]8169.

Links

Crossrefs

Cf. A105701, A072354, A105702, A105703, A105704, A105705, A105706, A105707, A105709.

Programs

  • Maple
    N:= 100: # for a(0)..a(N)
V:= Array(0..N): count:= 0:
for m from 1 while count < N+1 do
  v:= combinat:-fibonacci(m);
  L:= convert(v,base,10);
  S:= map(t -> t-1, select(t -> L[t]=8, [$1..nops(L)]));
  for s in S do if s <= N and V[s] = 0 then count:= count+1; V[s]:= m fi
od od:
convert(V,list); # Robert Israel, Apr 25 2021

A105701 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, 32, 25, 21, 34, 38, 61, 40, 60, 51, 61, 62, 64, 71, 88, 84, 88, 108, 103, 103, 112, 107, 129, 118, 138, 129, 131, 138, 148, 152, 155, 164, 166, 170, 176, 174, 181, 185, 204, 196, 198, 206, 212, 217, 217, 258, 240, 242, 244, 241, 248, 252, 259, 277, 265, 273
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

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

Examples

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

Links

Crossrefs

Cf. A000045, A072354.
Cf. A105702, A105703, A105704, A105705, A105706, A105707, A105708, A105709.

Programs

  • Maple
    N:= 100: # for a(0) to a(N)
F[0]:= 0: F[1]:= 1:
V:= Array(0..N):
count:= 1:
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]=0 and V[t]=0, [$0..min(N, nops(L)-1)]);
  count:= count + nops(M);
  V[M]:= m;
od:
V[0]:= 0:
convert(V, list); # Robert Israel, Jun 03 2020

Extensions

a(1) corrected by Robert Israel, Jun 03 2020

A105702 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

3, 8, 13, 18, 23, 35, 32, 37, 42, 47, 51, 56, 61, 66, 94, 75, 80, 85, 90, 102, 99, 104, 109, 114, 118, 123, 128, 133, 161, 142, 147, 152, 157, 166, 166, 171, 176, 184, 185, 190, 195, 200, 215, 209, 214, 219, 224, 233, 233, 238, 243, 251, 252, 257, 262, 267, 283
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

A105712(n) = A000045(a(n)).

Examples

			n=3: a(3)=18, A000045(18)=A105710(3)=2584->[2]584;
n=4: a(4)=23, A000045(23)=A105710(4)=28657->[2]8657.

Links

Crossrefs

Cf. A105701, A072354, A105703, A105704, A105705, A105706, A105707, A105708, A105709.

A105703 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

4, 9, 14, 45, 30, 28, 33, 38, 51, 53, 52, 57, 92, 95, 71, 76, 81, 98, 97, 95, 100, 105, 130, 119, 119, 124, 135, 143, 138, 143, 148, 185, 183, 162, 167, 172, 193, 181, 186, 191, 202, 209, 205, 210, 215, 227, 258, 229, 234, 239, 276, 248, 253, 258, 269, 283, 272
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

A105713(n) = A000045(a(n)).

Examples

			n=3: a(3)=45,
A000045(45)=A105710(3)=1134903170->113490[3]170;
n=4: a(4)=30, A000045(30)=A105710(4)=832040->8[3]2040.

Links

Crossrefs

Cf. A105701, A072354, A105702, A105704, A105705, A105706, A105707, A105708, A105709.

A105705 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, 10, 17, 25, 37, 29, 34, 52, 50, 56, 53, 58, 82, 98, 77, 77, 85, 92, 98, 96, 101, 125, 120, 127, 120, 125, 134, 144, 139, 144, 175, 159, 165, 163, 168, 180, 185, 216, 187, 192, 201, 210, 206, 211, 251, 250, 237, 230, 235, 246, 255, 275, 254, 261, 268, 305, 273
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

A105715(n) = A000045(a(n)).

Examples

			n=3: a(3)=25, A000045(25)=A105710(3)=75025->7[5]025;
n=4: a(4)=37, A000045(37)=A105710(4)=24157817->241[5]7817.

Links

Crossrefs

Cf. A105701, A072354, A105702, A105703, A105704, A105706, A105707, A105708, A105709.

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.

A105709 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

11, 17, 16, 50, 27, 36, 35, 66, 47, 55, 58, 59, 81, 70, 78, 83, 83, 95, 94, 111, 102, 148, 114, 140, 125, 126, 138, 137, 145, 150, 150, 163, 161, 183, 169, 205, 189, 191, 192, 193, 215, 204, 216, 212, 223, 224, 228, 243, 236, 250, 258, 257, 267, 260, 270, 271
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

A105719(n) = A000045(a(n)).

Examples

			n=3: a(3)=50,
A000045(50)=A105710(3)=12586269025->1258626[9]025;
n=4: a(4)=27, A000045(27)=A105710(4)=196418->1[9]6418.

Links

Crossrefs

Cf. A105701, A072354, A105702, A105703, A105704, A105705, A105706, A105707, A105708.

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.
Showing 1-10 of 10 results.

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