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 1-6 of 6 results.

A094400 Odd n dividing Fibonacci(n)-1 but neither Fibonacci(n-1) nor Fibonacci(n+1).

Original entry on oeis.org

7743, 27071, 54839, 72831, 217257, 388367, 417601, 575599, 670879, 691447, 701569, 809999, 850541, 881011, 1274897, 1365407, 1383249, 1464449, 1504097, 1653751, 1922817, 2106017, 2276351, 2385811, 2474047, 2556553, 2628879, 2697899, 2804543, 3017729, 3352049
Offset: 1

Views

Author

Eric Rowland, May 01 2004

Keywords

Links

Crossrefs

Cf. A069106, A069107, A094394, A094401, A094402.

Programs

  • Mathematica
    Select[Range[50000], OddQ[ # ] && Mod[Fibonacci[ # ] - 1, # ] == 0 && ! Mod[Fibonacci[ # - 1], # ] == 0 && ! Mod[Fibonacci[ # + 1], # ] == 0 &]

Extensions

Offset corrected by and a(15)-a(31) from Giovanni Resta, Jul 20 2013

A094411 Composite numbers k that divide both Fibonacci(k+1) and Fibonacci(k) + 1.

Original entry on oeis.org

5777, 10877, 75077, 80189, 100127, 113573, 161027, 162133, 231703, 430127, 618449, 635627, 667589, 851927, 1033997, 1106327, 1256293, 1388903, 1697183, 2263127, 2435423, 2512889, 2662277, 3175883, 3399527, 3452147, 3774377
Offset: 1

Views

Author

Eric Rowland, May 01 2004

Keywords

Comments

Also composites k that divide both Fibonacci(k+1) and Lucas(k) - 1. - Gary Detlefs, Feb 28 2013

Links

Crossrefs

Cf. A000032, A000045, A002808, A069107, A094395, A094401, A094412.

Programs

  • Mathematica
    Select[Range[2, 50000], ! PrimeQ[ # ] && Mod[Fibonacci[ # + 1], # ] == 0 && Mod[Fibonacci[ # ] + 1, # ] == 0 &]

Extensions

More terms from Gareth McCaughan, Jun 11 2004
More terms from Ryan Propper, Aug 04 2005
Offset corrected by Giovanni Resta, Jul 20 2013

A094412 Numbers k that divide Fibonacci(k+1) but do not divide Fibonacci(k) + 1.

Original entry on oeis.org

323, 377, 2834, 3827, 6479, 11663, 18407, 19043, 20999, 23407, 25877, 27323, 34943, 35207, 39203, 44099, 47519, 50183, 51983, 53663, 60377, 65471, 78089, 79547, 81719, 82983, 84279, 84419, 86063, 90287, 94667, 104663, 109871, 121103, 121393
Offset: 1

Views

Author

Eric Rowland, May 01 2004

Keywords

Links

Crossrefs

Cf. A000045, A069107, A094395, A094401, A094411.

Programs

  • Mathematica
    Select[Range[50000], ! Mod[Fibonacci[ # ] + 1, # ] == 0 && Mod[Fibonacci[ # + 1], # ] == 0 &]
Select[Range[122000],Divisible[{Fibonacci[#+1],Fibonacci[#]+1},#]=={True,False}&] (* Harvey P. Dale, Apr 16 2019 *)
  • PARI
    fibmod(n,m)=(Mod([0,1;1,1],m)^n*[0;1])[1,1]
is(n)=fibmod(n+1,n)==0 && fibmod(n,n)!=-1 \\ Charles R Greathouse IV, Nov 04 2016

A319168 Frobenius pseudoprimes == 1,4 (mod 5) with respect to Fibonacci polynomial x^2 - x - 1.

Original entry on oeis.org

4181, 6721, 13201, 15251, 34561, 51841, 64079, 64681, 67861, 68251, 90061, 96049, 97921, 118441, 146611, 163081, 186961, 197209, 219781, 252601, 254321, 257761, 268801, 272611, 283361, 302101, 303101, 330929, 399001, 433621, 438751, 489601, 512461, 520801
Offset: 1

Views

Author

Jianing Song, Sep 12 2018

Keywords

Comments

Complement of A212423 with respect to A212424.
Intersection of A212424 and A047209.
Composite k == 1,4 (mod 5) such that Fibonacci(k) == 1 (mod k) and that k divides Fibonacci(k-1).

Examples

			4181 = 37*113 is composite, while Fibonacci(4180) == 0 (mod 4181), Fibonacci(4181) == 1 (mod 4181), so 4181 is a term.

Links

Crossrefs

Cf. A047209, A093372, A094394, A094401, A212423, A212424.

Programs

  • PARI
    for(n=2,500000,if(!isprime(n) && (n%5==1||n%5==4) && fibonacci(n-kronecker(5,n))%n==0 && (fibonacci(n)-kronecker(5,n))%n==0, print1(n, ", ")))

A095399 Modified juggler modified further: a[n]=(1-Mod[n,2])*Floor[n^(3/4)]+Mod[n,2]*Floor[n^(4/3)]; original exponents {1/2,3/2} are replaced with {3/4,4/3}.

Original entry on oeis.org

1, 1, 4, 2, 8, 3, 13, 4, 18, 5, 24, 6, 30, 7, 36, 8, 43, 8, 50, 9, 57, 10, 65, 10, 73, 11, 81, 12, 89, 12, 97, 13, 105, 14, 114, 14, 123, 15, 132, 15, 141, 16, 150, 17, 160, 17, 169, 18, 179, 18, 189, 19, 199, 19, 209, 20, 219, 21, 229, 21, 240, 22, 250, 22, 261, 23, 272, 23
Offset: 1

Views

Author

Labos Elemer, Jun 18 2004

Keywords

Crossrefs

Cf. A007320, A094683, A094716, A094396-A094401.

Programs

  • Mathematica
    e[x_]:=e[x]=(1-Mod[x, 2])*Floor[N[x^(3/4), 50]] +Mod[x, 2]*Floor[N[x^(4/3), 50]];e[1]=1; Table[e[w], {w, 1, 150}]

A095400 Largest value in trajectory when the following modified juggler map is iterated: a[n]=(1-Mod[n, 2])*Floor[n^(3/4)]+Mod[n, 2]*Floor[n^(4/3)]; original exponents {1/2, 3/2} are replaced with {3/4, 4/3}.

Original entry on oeis.org

1, 2, 4, 4, 8, 6, 30, 8, 18, 10, 24, 12, 30, 30, 36, 16, 150, 18, 50, 20, 1320, 22, 43366048, 24, 26092, 26, 350, 28, 41678, 30, 234421146, 32, 2438232, 34, 114, 36, 5184, 38, 132, 40, 124026, 42, 150, 150, 160, 150, 934, 48, 1008, 50, 1084, 52, 12202, 54, 1240, 56
Offset: 1

Views

Author

Labos Elemer, Jun 18 2004

Keywords

Examples

			n=101: the trajectory is {101, 470, 100, 31, 97, 445, 3397, 51065, 1894513, 234421146, 1894512, 51064, 3396, 444, 96, 30, 12, 6, 3, 4, 2, 1}, peak=a[101]=234421146.

Crossrefs

Cf. A007320, A094683, A094716, A094396-A094401.

Programs

  • Mathematica
    e[x_]:=e[x]=(1-Mod[x, 2])*Floor[N[x^(3/4), 50]] +Mod[x, 2]*Floor[N[x^(4/3), 50]];e[1]=1; fe[x_]:=Delete[FixedPointList[e, x], -1]; Table[Max[fe[w]], {w, 1, 150}]
Showing 1-6 of 6 results.

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