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 1-9 of 9 results.

A134789 a(n) = round(Fibonacci(prime(k))/prime(k)), where k = A119984(n).

Original entry on oeis.org

1, 1, 2, 8, 18, 94, 1246, 17732, 10081266, 63217342, 1195118711985006, 8140003186959622868813528, 139669360584622467747806014, 1324290912910022899017738237233285189213652972190967113265372469016533360
Offset: 1

Views

Author

Artur Jasinski, Nov 12 2007

Keywords

Links

Crossrefs

Cf. A000045, A050937, A090819, A119984, A134787, A134788.

Programs

  • Mathematica
    k = {}; Do[If[PrimeQ[Fibonacci[Prime[n]]], AppendTo[k, Round[Fibonacci[Prime[n]]/Prime[n]]]], {n, 1, 100}]; k

A134791 a(n) = floor(log(Fibonacci(prime(k))/prime(k))), where k = A119984(n).

Original entry on oeis.org

-1, 0, 0, 2, 2, 4, 7, 9, 16, 17, 34, 57, 60, 166, 200, 201, 209, 237, 266, 267, 1420, 2263, 2582, 4470, 4646, 6933, 12289, 14789, 17311, 18039, 24449, 39369, 50472, 62555, 71250, 96762, 191209, 208726, 283920, 285676, 290979, 448242, 505208, 618634, 787250, 867638
Offset: 1

Views

Author

Artur Jasinski, Nov 12 2007

Keywords

Links

Crossrefs

Cf. A000045, A050937, A090819, A119984, A134787, A134788, A134789, A134790, A134792.

Programs

  • Mathematica
    k = {}; Do[If[PrimeQ[Fibonacci[Prime[n]]], AppendTo[k, Floor[Log[Fibonacci[Prime[n]]/Prime[n]]]]], {n, 1, 200}]; k

Extensions

a(21)-a(46) from Amiram Eldar, Oct 13 2024

A134792 a(n) = round(log(Fibonacci(prime(k))/prime(k))), where k = A119984(n).

Original entry on oeis.org

0, 0, 1, 2, 3, 5, 7, 10, 16, 18, 35, 57, 60, 166, 201, 201, 209, 238, 267, 268, 1421, 2263, 2583, 4471, 4647, 6934, 12289, 14789, 17312, 18039, 24450, 39370, 50472, 62555, 71250, 96762, 191210, 208727, 283921, 285676, 290980, 448242, 505208, 618634, 787251, 867638
Offset: 1

Views

Author

Artur Jasinski, Nov 12 2007

Keywords

Links

Crossrefs

Cf. A000045, A050937, A090819, A119984, A134787, A134788, A134789, A134790, A134791.

Programs

  • Mathematica
    k = {}; Do[If[PrimeQ[Fibonacci[Prime[n]]], AppendTo[k, Round[Log[Fibonacci[Prime[n]]/Prime[n]]]]], {n, 1, 200}]; k

Extensions

a(21)-a(46) from Amiram Eldar, Oct 13 2024

A122534 Numbers k such that Fibonacci(prime(prime(k))) is prime.

Original entry on oeis.org

1, 2, 3, 4, 9, 23, 25, 1456, 1616, 3865
Offset: 1

Views

Author

Alexander Adamchuk, Sep 18 2006

Keywords

Comments

The corresponding primes are {2,5,89,1597,99194853094755497,...}.
Numbers k such that A093308(k) is prime.
A277575(n) = prime(a(n)) is a prime in A119984.

Crossrefs

Cf. A000040, A000045, A119984, A083668, A093308, A075737, A001605, A006450, A005478, A030426, A277284, A277575.

Formula

a(n) = PrimePi(A277575(n)) = PrimePi(PrimePi(A277284(n))). - Bobby Jacobs, Oct 26 2016

A123677 Primes p such that Lucas(prime(p)) is prime, where Lucas = A000032.

Original entry on oeis.org

3, 5, 7, 11, 13, 71, 113, 643, 769, 13681, 51929
Offset: 1

Views

Author

Alexander Adamchuk, Oct 05 2006

Keywords

Comments

These are the primes in A120561.
Numbers n such that Lucas(prime(n)) is prime are listed in A120561; indices of prime Lucas numbers are listed in A001606.

Crossrefs

Cf. A000032, A123678, A120561, A001606, A119984, A122534, A277290.

Formula

a(n) = prime(A123678(n)).
a(n) = pi(A277290(n)). - Bobby Jacobs, Oct 30 2016

Extensions

51929 found by Henri Lifchitz, from Jens Kruse Andersen, Jul 24 2014

A123678 Numbers n such that Lucas(prime(prime(n))) is prime, where Lucas(k) = A000032(k).

Original entry on oeis.org

2, 3, 4, 5, 6, 20, 30, 117, 136, 1616, 5313
Offset: 1

Views

Author

Alexander Adamchuk, Oct 05 2006

Keywords

Comments

Indices of prime Lucas numbers are listed in A001606.
Numbers n such that Lucas(prime(n)) is prime are listed in A120561.
Primes in A120561 are listed in A123677(n) = prime(a(n)).

Crossrefs

Cf. A000032, A123677, A120561, A001606, A277290.
Cf. A119984, A122534 (Numbers n such that Fibonacci(prime(prime(n))) is prime).

Formula

a(n) = pi(A123677(n)).
a(n) = pi(pi(A277290(n))). - Bobby Jacobs, Oct 30 2016

Extensions

5313 found by Henri Lifchitz, from Jens Kruse Andersen, Jul 24 2014

A120561 Numbers n such that Lucas(prime(n)) is prime, where Lucas = A000032.

Original entry on oeis.org

1, 3, 4, 5, 6, 7, 8, 11, 12, 13, 15, 16, 18, 20, 22, 30, 65, 71, 96, 112, 113, 150, 184, 218, 643, 645, 769, 982, 1059, 1304, 1464, 1649, 1695, 2208, 3776, 3899, 4626, 5236, 5684, 7988, 8700, 9143, 13013, 13681, 14641, 16590, 17433, 18198, 29529, 32870, 37234, 43994, 47150, 50373, 51420, 51929, 52953, 55965, 71398, 82258
Offset: 1

Views

Author

Alexander Adamchuk, Aug 07 2006, Oct 05 2006

Keywords

Comments

All prime Lucas numbers A000032[n] have indices that are prime, zero or a power of 2. It is a conjecture that all indices of prime Lucas numbers are prime, except n = 0, 4, 8, 16.
Indices of prime Lucas numbers are listed in A001606[n] = {0,2,4,5,7,8,11,13,16,17,19,31,37,41,47,53,61,...}.
Primes in a(n) are listed in A123677[n] = {3,5,7,11,13,71,113,643,769,13681,...} Primes p such that Lucas[Prime[p]] is prime.
Numbers n such that Lucas[Prime[Prime[n]]] is prime are listed in A123678[n] = PrimePi[A123677[n]] = {2,3,4,5,6,20,30,117,136,1616,...}.

Crossrefs

Cf. A000032, A119984. Cf. A001606 - Indices of prime Lucas numbers.
Cf. A123677, A123678.

Programs

  • Mathematica
    Select[ Range[300], PrimeQ[ Fibonacci[ Prime[ # ] - 1 ] + Fibonacci[ Prime[ # ] + 1 ]] & ]

Formula

a(n) = PrimePi(A001606(n+4)) for n>5.

Extensions

a(52)-a(60) (from A001606) from Jens Kruse Andersen, Jul 24 2014

A277575 Primes p such that Fibonacci(prime(p)) is prime.

Original entry on oeis.org

2, 3, 5, 7, 23, 83, 97, 12161, 13681, 36467
Offset: 1

Views

Author

Bobby Jacobs, Oct 20 2016

Keywords

Comments

Suggested by Alexander Adamchuk in A122534.

Crossrefs

Primes in A119984.
Cf. A000040, A000045, A001605, A005478, A006450, A030426, A075737, A083668, A093308, A122534, A277284.

Programs

  • PARI
    isok(p) = isprime(p) && isprime(fibonacci(prime(p))); \\ Michel Marcus, Oct 22 2016

Formula

a(n) = prime(A122534(n)).
a(n) = PrimePi(A277284(n)).

A339173 Index of record values of A339082.

Original entry on oeis.org

1, 3, 5, 9, 11, 15, 21, 27, 41, 45, 81, 129, 135, 357, 429, 431, 447, 507, 567, 569, 2969, 4721, 5385, 9309, 9675, 14429, 25559, 30755, 35997, 37509, 50831, 81837, 104909, 130019, 148089, 201105, 397377, 433779, 590039, 593687, 604709, 931515, 1049895, 1285605, 1636005, 1803057, 1968719, 2904351, 3244367, 3340365
Offset: 1

Views

Author

Chai Wah Wu, Nov 25 2020

Keywords

Comments

Also index of record values of A335568.

Crossrefs

Cf. A000040, A000045, A001605, A005478, A119984, A245306, A335568, A338762, A338794.

Formula

A339082(a(n)) = A119984(n).
For n > 1, a(n) = A001605(n+1)-2.
Showing 1-9 of 9 results.

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