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 12 results. Next

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

A050815 Number of positive Fibonacci numbers with n decimal digits.

Original entry on oeis.org

6, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1999

Keywords

Comments

If n>1 then a(n) = 4 or 5. - Robert Gerbicz, Sep 05 2002
The sequence is almost periodic, see also A072353. - Reinhard Zumkeller, Apr 14 2005

Examples

			At length 1 there are 6 such numbers: 1, 1, 2, 3, 5 and 8.

Links

Crossrefs

See A098842 for another version.
Cf. A000045, A001622, A002390, A072354, A105563, A105565, A060384, A097348.

Programs

  • Mathematica
    Drop[Last/@Tally[Table[IntegerLength[Fibonacci[n]],{n,505}]],-1] (* Jayanta Basu, Jun 01 2013 *)

Formula

Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = log(10)/log(phi) = 1/A097348 = 4.7849719667... - Amiram Eldar, Jan 12 2022
For n>1, a(n) = 4+[{n*alpha+beta}<{alpha}], where alpha=log(10)/log(phi), beta=log(5)/(2*log(phi)), [X] is the Iverson bracket, {x}=x-floor(x), denotes the fractional part of x, and phi=(1+sqrt(5))/2. - Hans J. H. Tuenter, Jul 20 2025
a(n) = A072354(n+1)-A072354(n), a first-order difference. - Hans J. H. Tuenter, Jul 20 2025

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.

A105704 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

9, 12, 27, 19, 24, 43, 36, 74, 43, 48, 60, 72, 62, 67, 72, 79, 92, 86, 91, 108, 104, 112, 110, 115, 122, 152, 129, 134, 143, 146, 164, 153, 158, 171, 171, 179, 177, 182, 189, 202, 196, 201, 210, 213, 246, 220, 225, 257, 238, 244, 244, 249, 256, 266, 263, 268
Offset: 0

Views

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

Comments

A105714(n) = A000045(a(n)).

Examples

			n=3: a(3)=19, A000045(19)=A105710(3)=4181->[4]181;
n=4: a(4)=24, A000045(24)=A105710(4)=46368->[4]6368.

Links

Crossrefs

Cf. A105701, A072354, A105702, A105703, 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.
Showing 1-10 of 12 results. Next

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