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.

A171980 Prime divisors of elements of A129066.

Original entry on oeis.org

5, 3001, 120041, 532501, 720241, 2160721, 3937501, 9375001, 16505501, 120040001, 158453021, 165055001, 202567501, 289312501, 562500061, 900307501, 985937501, 1500512501, 1512504701, 3169060421, 3301100021, 3908604433, 3993757501
Offset: 1

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Author

Max Alekseyev, Jan 20 2010

Keywords

Comments

Corresponding smallest multiples from A129066 are given in A171981.
Prime p>5 is in this sequence if the multiplicative order of (sqrt(5)-3)/2 modulo p is the product of smaller terms of this sequence.

Links

Crossrefs

Cf. A057719, A066364, A129729, A171981

A171981 Smallest multiples from A129066 of primes from A171980.

Original entry on oeis.org

5, 75025, 9006076025, 332813125, 54036081025, 162108093025, 12304690625, 3662109765625, 1238325212525, 225150026875625, 8562180281412026525, 309581286250625, 15197626762525, 4520507828125, 2059936966552758203125
Offset: 1

Views

Author

Max Alekseyev, Jan 20 2010

Keywords

Comments

A129066 lists integers n such that n divides n-th Fibonacci number A000045(n) with multiples of 12 excluded, while A171980 lists possible prime divisors of elements of A129066 in the increasing order. This sequence lists smallest multiples from A129066 of primes from A171980.

Crossrefs

Cf. A114207, A140258

Formula

a(n) = min { A129066(m) : A171980(n)|A129066(m) }

A072378 Numbers n such that 12*n divides F(12*n), where F(m) is the m-th Fibonacci number.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 25, 27, 28, 30, 32, 36, 40, 42, 45, 46, 48, 50, 51, 54, 55, 56, 57, 60, 64, 70, 72, 75, 80, 81, 84, 90, 92, 96, 98, 100, 102, 108, 110, 112, 114, 120, 125, 126, 128, 135, 138, 140, 144, 150, 153, 155, 160, 162, 165
Offset: 1

Views

Author

Omar Antolin Camarena (omar(AT)tlahui.posgrado.unam.mx), Jul 19 2002

Keywords

Comments

Odd integers n such that n divides the n-th Fibonacci number form sequence A129066, while even such n's are multiples of 12.
a(n) seems to be asymptotic to a constant multiple of n^phi, where phi is the golden ratio.

Examples

			3 belongs to the sequence because 3*12=36 divides F(36) = 14930352. For every n, 5^n belongs to the sequence, as can be proved by induction.

Links

Crossrefs

Cf. A128974, A317971.

Programs

  • Mathematica
    Select[Range[n], Mod[Fibonacci[12# ], 12# ]==0&]

Extensions

Edited by Max Alekseyev, Jan 21 2010
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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