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 1-4 of 4 results.

A105800 Greatest Fibonacci number that is a proper divisor of the n-th Fibonacci number; a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 3, 2, 5, 1, 8, 1, 13, 5, 21, 1, 34, 1, 55, 13, 89, 1, 144, 5, 233, 34, 377, 1, 610, 1, 987, 89, 1597, 13, 2584, 1, 4181, 233, 6765, 1, 10946, 1, 17711, 610, 28657, 1, 46368, 13, 75025, 1597, 121393, 1, 196418, 89, 317811, 4181, 514229, 1, 832040, 1
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 20 2005

Keywords

Comments

a(A001605(n)) = 1.

Links

Crossrefs

Cf. A000045, A032742, A076984, A139045, A280686, A280688, A280689, A280690, A280698, A280699.
Cf. A046022 (gives the positions of ones).

Programs

  • Mathematica
    nn=70;Join[{1,1},With[{fibs=Fibonacci[Range[nn]]},Table[ Max[ Intersection[ Most[Divisors[fibs[[n]]]],fibs]],{n,3,nn}]]] (* Harvey P. Dale, Apr 10 2012 *)

Formula

From Antti Karttunen, Jan 11 2017: (Start)
a(n) = A280686(A000045(n)).
a(n) = A000045(A032742(n)). [Because A000045 is a divisibility sequence.]
a(A032742(n)) = A280688(n).
(End)

A280690 a(n) = A000045(n) / A105800(n); the n-th Fibonacci number divided by its largest Fibonacci proper divisor.

Original entry on oeis.org

1, 1, 2, 3, 5, 4, 13, 7, 17, 11, 89, 18, 233, 29, 122, 47, 1597, 76, 4181, 123, 842, 199, 28657, 322, 15005, 521, 5777, 843, 514229, 1364, 1346269, 2207, 39602, 3571, 709805, 5778, 24157817, 9349, 271442, 15127, 165580141, 24476, 433494437, 39603, 1860497, 64079, 2971215073, 103682, 598364773, 167761, 12752042, 271443
Offset: 1

Views

Author

Antti Karttunen, Jan 11 2017

Keywords

Comments

A000045 is a divisibility sequence.

Links

Crossrefs

Cf. A000045, A032742, A105800, A280687, A280689.

Formula

a(n) = A000045(n) / A105800(n) = A000045(n) / A000045(A032742(n)).
a(n) = A280687(A000045(n)).
Other identities. For all n >= 1:
a(A032742(n)) = A280689(n).

A280688 a(n) = A000045(A054576(n))= A280686(A105800(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 5, 1, 1, 1, 8, 1, 1, 2, 13, 1, 5, 1, 21, 1, 1, 1, 34, 1, 1, 1, 55, 1, 13, 1, 89, 5, 1, 1, 144, 1, 5, 1, 233, 1, 34, 1, 377, 1, 1, 1, 610, 1, 1, 13, 987, 1, 89, 1, 1597, 1, 13, 1, 2584, 1, 1, 5, 4181, 1, 233, 1, 6765, 34, 1, 1, 10946, 1, 1, 1, 17711, 1, 610, 1, 28657, 1, 1, 1, 46368, 1, 13, 89, 75025, 1, 1597
Offset: 1

Views

Author

Antti Karttunen, Jan 11 2017

Keywords

Links

Crossrefs

Cf. A000045, A032742, A054576, A105800, A280686, A280689.

Formula

a(n) = A000045(A054576(n)).
a(n) = A280686(A105800(n)).
a(n) = A105800(A032742(n)).

A280691 a(n) = A015518(A032742(n)) / A015518(A054576(n)).

Original entry on oeis.org

1, 1, 1, 2, 1, 7, 1, 10, 7, 61, 1, 26, 1, 547, 61, 82, 1, 703, 1, 242, 547, 44287, 1, 730, 61, 398581, 703, 2186, 1, 58807, 1, 6562, 44287, 32285041, 547, 19682, 1, 290565367, 398581, 59050, 1, 4780783, 1, 177146, 58807, 23535794707, 1, 531442, 547, 3472494301, 32285041, 1594322, 1, 387400807, 44287, 4782970, 290565367, 17157594341221, 1, 14348906, 1
Offset: 1

Views

Author

Antti Karttunen, Jan 11 2017

Keywords

Comments

A015518 is a divisibility sequence, which guarantees that the result of the division is an integer.
a(n) is a function of A032742(n).

Links

Crossrefs

Cf. A015518, A032742, A054576.
Cf. also A280689.

Programs

Formula

a(n) = A015518(A032742(n)) / A015518(A054576(n)).
Showing 1-4 of 4 results.

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