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 1-3 of 3 results.

A182212 a(n) = floor(n! / Fibonacci(n)).

Original entry on oeis.org

1, 2, 3, 8, 24, 90, 387, 1920, 10672, 65978, 448503, 3326400, 26725411, 231242151, 2143728472, 21198368680, 222722246772, 2477698802526, 29094738198716, 359630747697951, 4667544506825273, 63463425429259086, 902118740233973431, 13380961044971520000
Offset: 1

Views

Author

Alex Ratushnyak, Apr 19 2012

Keywords

Examples

			a(7) = floor(7! / Fibonacci[7]) = floor(5040/13) = 387. - _T. D. Noe_, Apr 19 2012

Crossrefs

Cf. A182213, A000045, A000142.

Programs

  • Mathematica
    Table[Floor[n!/Fibonacci[n]], {n, 50}] (* T. D. Noe, Apr 19 2012 *)
  • Python
    prpr = 0
prev = 1
fa = 1
for i in range(2,26):
    print(fa//prev, end=',')
    fa *= i
    current = prev + prpr
    prpr = prev
    prev = current

Formula

a(n) = floor(A000142(n) / A000045(n)) = floor( n! / fibonacci(n) ), n>0.

A262348 a(n) = A000215(n) mod A000045(n).

Original entry on oeis.org

0, 0, 1, 2, 2, 1, 10, 17, 19, 17, 5, 17, 75, 17, 257, 983, 987, 1481, 4178, 4652, 7433, 3488, 10665, 19169, 51372, 538, 257, 65537, 422030, 17, 111134, 430622, 592107, 1036631, 4104877, 11311649, 4963932, 23430341, 16834037, 65537, 67016878, 53547017, 316617399
Offset: 1

Views

Author

Ilya Gutkovskiy, Sep 18 2015

Keywords

Links

Crossrefs

Cf. A000045, A000215, A182213, A246846.

Programs

  • Magma
    [(2^(2^n) + 1) mod(Fibonacci(n)): n in [1..29]]; // Vincenzo Librandi, Sep 19 2015
  • Mathematica
    f[n_] := Mod[ PowerMod[2, 2^n, Fibonacci[n]] + 1, Fibonacci[n]]; Array[f, 43] (* Robert G. Wilson v, Sep 18 2015 *)
  • PARI
    a(n) = my (fn = fibonacci(n)); lift(Mod(Mod(2, fn)^(2^n) + 1, fn)); \\ Michel Marcus, Sep 19 2015

Extensions

More terms from Robert G. Wilson v, Sep 18 2015

A332409 a(n) = n!! mod Fibonacci(n).

Original entry on oeis.org

0, 0, 1, 2, 0, 0, 1, 6, 27, 45, 71, 0, 228, 73, 605, 861, 956, 2376, 1199, 5235, 7137, 5017, 21617, 40320, 49250, 72900, 94129, 253071, 125204, 188760, 786046, 1041600, 3306329, 2717231, 8692580, 4869072, 10661888, 33618132, 14333453, 66880275, 110783982
Offset: 1

Views

Author

Andrew Nelson, Feb 17 2020

Keywords

Comments

a(n) = 0 for n = 1, 2, 5, 6, 12 (a(n) < 500).

Examples

			For n = 1, a(1) = 1!! mod Fibonacci(1) = 1 mod 1 = 0.
For n = 4, a(4) = 4!! mod Fibonacci(4) = 8 mod 3 = 2.

Crossrefs

Cf. A000045, A006882, A182213.

Programs

  • Mathematica
    Table[Mod[n!!,Fibonacci[n]],{n,50}] (* Harvey P. Dale, Sep 08 2020 *)
  • PARI
    a0(n) = my(f=fibonacci(n)); prod(i=0, (n-1)\2, n - 2*i) % f; \\ Michel Marcus, Mar 17 2020

Formula

a(n) = n!! mod Fibonacci(n).
where n!! denotes the double factorial of n (n!! = n*a(n-2) for n > 1, a(0) = a(1) = 1), and Fibonacci(n) denotes the n-th Fibonacci number.
Showing 1-3 of 3 results.

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