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.

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

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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

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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

A277290 Prime-indexed primes p such that Lucas(p) is prime.

Original entry on oeis.org

5, 11, 17, 31, 41, 353, 617, 4787, 5851, 148091, 637751
Offset: 1

Views

Author

Bobby Jacobs, Oct 21 2016

Keywords

Examples

			17 = A000040(7), with 7 itself being a prime, and A000032(17) = 3571, a prime, thus 17 is included in this sequence.

Crossrefs

Cf. A000032, A000040, A123677, A123678.
Subsequence of A006450. See also A168033.

Formula

a(n) = prime(A123677(n)).
a(n) = prime(prime(A123678(n))).
Showing 1-3 of 3 results.

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