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.

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

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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

Formula

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

A087807 Prime factors of solutions to 24^n == 1 (mod n).

Original entry on oeis.org

23, 47, 14759, 49727, 124799, 304751, 497261, 609503, 1828507, 2685259, 10741037, 12872687, 13877879, 23462213, 23652649, 27755759, 29134267, 31908959, 53753807, 65205263, 132771091, 218148653, 341965703, 551361983, 734951759
Offset: 1

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Author

Thomas Baruchel, Oct 14 2003

Keywords

Comments

Primes that divide at least one term of A014960.
Prime p is in this sequence iff the multiplicative order of 24 modulo p is the product of smaller terms of this sequence. - Max Alekseyev, May 26 2010

Examples

			A014960(12) = 2870377 = 23 * 124799
		

Crossrefs

Extensions

Corrected and extended by Max Alekseyev, May 26 2010
Edited by Max Alekseyev, Nov 16 2019

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

A354026 Primes that divide some k dividing 4^k + 3^k (A045584).

Original entry on oeis.org

7, 379, 14407, 689431, 4235659, 41647747, 137534083, 239900179, 242121643, 349909477, 1245283747, 1478065891, 1605314383, 2500276549, 2748751303, 5618210347, 7490947129, 11236420693, 11260421089, 16948514941, 29440659361, 74163546829, 75093609319, 82188727303
Offset: 1

Views

Author

Max Alekseyev, May 15 2022

Keywords

Comments

Prime p > 3 is in this sequence iff all prime factors of the multiplicative order of -3/4 modulo p belong to this sequence.

Crossrefs

Programs

  • PARI
    S=[]; forprime(p=5,oo, f=Set(factor(znorder(Mod(-3/4,p)))[,1]); if(#setintersect(S,f)==#f, S=setunion(S,[p]); print1(p,", ")));

Extensions

a(18)-a(24) from Jinyuan Wang, Jan 29 2025
Showing 1-4 of 4 results.