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

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).

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.

A106700 Numbers k such that 9973*k - 1009 is prime.

Original entry on oeis.org

32, 72, 74, 90, 92, 96, 102, 104, 114, 116, 120, 144, 156, 200, 210, 216, 230, 236, 242, 260, 270, 272, 294, 296, 312, 314, 324, 326, 336, 344, 354, 386, 432, 450, 456, 464, 476, 494, 516, 522, 530, 546, 566, 600, 620, 630, 632, 660, 686, 714, 716, 726, 734
Offset: 1

Views

Author

Parthasarathy Nambi, May 13 2005

Keywords

Comments

1009 and 9973 are the smallest and largest of four-digit primes.

Examples

			If k=32, then 9973*k - 1009 = 318127 (prime).
If k=116, then 9973*k - 1009 = 1155859 (prime).

Links

Crossrefs

Cf. A105680, A105710.

Programs

A106699 Numbers k such that 1009*k - 9973 is prime.

Original entry on oeis.org

14, 24, 30, 48, 74, 78, 86, 108, 116, 128, 146, 168, 176, 188, 200, 204, 216, 234, 240, 248, 266, 294, 300, 308, 314, 318, 330, 350, 380, 386, 396, 410, 420, 468, 470, 480, 494, 510, 524, 534, 536, 554, 576, 584, 590, 596, 620, 630, 636, 648, 650, 666, 680
Offset: 1

Views

Author

Parthasarathy Nambi, May 13 2005

Keywords

Comments

1009 and 9973 are the smallest and largest of four-digit primes.

Examples

			If k=14, then 1009*k - 9973 = 4153 (prime).
If k=128, then 1009*k - 9973 = 119179 (prime).

Crossrefs

Cf. A105680, A105710.

Programs

Showing 1-10 of 10 results.

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