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.

Crossrefs

A129066 Numbers k such that k divides Fibonacci(k) with multiples of 12 excluded.

Original entry on oeis.org

1, 5, 25, 125, 625, 3125, 15625, 75025, 78125, 375125, 390625, 1875625, 1953125, 9378125, 9765625, 46890625, 48828125, 234453125, 244140625, 332813125, 1172265625, 1220703125, 1664065625, 5628750625, 5861328125, 6103515625, 8320328125, 9006076025
Offset: 1

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Author

Alexander Adamchuk, May 11 2007

Keywords

Comments

Set difference of A023172 and 12*A072378.
The sequence is closed under multiplication.
Also, if m is in this sequence (i.e., gcd(F(m),m)=m) then F(m) is in this sequence (since gcd(F(F(m)),F(m)) = F(gcd(F(m),m)) = F(m)).
In particular, this sequence includes all terms of geometric progressions 5^k*Fibonacci(5^m) for integers k >= 0 and m >= 0.

Examples

			a(1) = Fibonacci(1) = 1,
a(2) = Fibonacci(5) = 5,
a(3)..a(7) = {5^2, 5^3, 5^4, 5^5, 5^6},
a(8) = 75025 = 5^2*3001 = Fibonacci(5^2),
a(9) = 5^7,
a(10) = 375125 = 5^3*3001 = 5*Fibonacci(5^2),
a(11) = 5^8.
		

Crossrefs

Prime divisors are given in A171980. Their smallest multiples are given in A171981.

Programs

  • Mathematica
    Do[ If[ !IntegerQ[ n/12 ] && IntegerQ[ Fibonacci[n] / n ], Print[n] ], {n,1,5^8} ]
  • PARI
    is(n)=n%12 && (Mod([0,1;1,1],n)^n*[0;1])[1,1]==0 \\ Charles R Greathouse IV, Nov 04 2016

Extensions

Edited and extended by Max Alekseyev, Sep 20 2009
a(1)=1 added by Zak Seidov, Nov 01 2009
Edited and extended by Max Alekseyev, Jan 20 2010

A354027 Smallest k dividing 3^k + 4^k that have divisor A354026(n).

Original entry on oeis.org

7, 2653, 4941601, 236474833, 20930936750059, 4899815786803, 330219333283, 4455186224209, 9770481627816301, 351829430300299, 26064955344333473991073, 192144131632327, 3006539977771582357, 2059085249993107, 13468375028434716454309, 1753571527639980559, 2338095370082599813
Offset: 1

Views

Author

Max Alekseyev, May 15 2022

Keywords

Comments

Smallest term of A045584 divisible by prime A354026(n).

Crossrefs

Showing 1-3 of 3 results.