A001606 -id:A001606 - cp's OEIS frontend

A216575 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 10*b^2.

5, 13, 17, 37, 41, 53, 61, 113, 313, 353, 613, 617, 1097, 1361, 4793, 7741, 14449, 19469, 35449, 51169, 89849, 140057, 159521, 183089, 193201, 344293, 387433, 443609, 532277, 631181, 651821

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

A290246 Prime numbers that are common indices to both prime Lucas and prime Wagstaff numbers.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 31, 61, 79, 313, 10691

Offset: 1

Amiram Eldar, Jul 24 2017

Prime numbers p such that Lucas(p) and (2^p + 1)/3 are both primes.

Intersection of A000978 and A001606.

Cf. A000978, A001606, A080327.

seq = {}; wagstaff[n_] := (2^n + 1)/3; Do[p = Prime[n]; If[PrimeQ[LucasL[p]] && PrimeQ[wagstaff[p]], AppendTo[seq, p]], {n, 1, 1304}]; seq

A330777 Numbers k such that k and Lucas(k) have the same number of divisors.

Original entry on oeis.org

1, 2, 5, 7, 10, 11, 13, 14, 17, 19, 24, 26, 28, 31, 37, 38, 40, 41, 47, 53, 61, 62, 71, 79, 86, 88, 113, 152, 178, 202, 248, 313, 353, 458, 488, 503, 586, 613, 617, 856, 863, 914, 1082, 1097, 1306, 1318, 1361, 1784

Offset: 1

Chai Wah Wu, Dec 31 2019

All prime terms of A001606 (i.e., terms in A001606 that are not nontrivial powers of 2) are terms of this sequence.
Conjecture: all terms are of the form 2^k*p for k >= 0 and p prime.
It is unknown whether 1816 is a term (the smallest number for which membership in the sequence is unknown); it depends on whether Lucas(1816)/47 is a semiprime or not. The following composite numbers are terms of the sequence: 3106, 3928, 4006, 5414, 5498, 14318, 20578. - Chai Wah Wu, Jan 03 2020

Blair Kelly, Fibonacci and Lucas Factorizations.

Cf. A000032, A001606, A080651.

Select[Range[100],DivisorSigma[0,#]==DivisorSigma[0,LucasL[#]]&] (* Metin Sariyar, Jan 03 2020 *)

for(k=1,320,if(numdiv(k)==numdiv(fibonacci(k+1)+fibonacci(k-1)),print1(k,", "))) \\ Hugo Pfoertner, Jan 03 2020

A377183 Positive numbers k such that L(k)-1 is prime, where L(k) is the k-th Lucas number.

Original entry on oeis.org

2, 3, 6, 24, 48, 96

Offset: 1

Harsh Aggarwal, Oct 18 2024

Terms must be 3-smooth. All other terms have trivial factors. No other terms under 10^7 (a(7) > 10^7).

			24 is a term because L(24)-1 = 103681 which is prime. Also 24 = 2^2*3^1.

Indices of primes in A001610.

Cf. A000032, A000204, A001606.

A377184 Numbers k such that L(k)+1 is prime, where L(k) is the k-th Lucas number.

Original entry on oeis.org

0, 1, 3, 6, 18

Offset: 1

Harsh Aggarwal, Oct 18 2024

Positive terms must be a power of 3 or twice a power of 3. All other terms have trivial factors. No other terms under 10^7 (a(6) > 10^7).

			18 is a term because L(18)+1 = 5779 which is prime. Also 18 = 2*3^2.

Indices of primes in A001612.

Cf. A000032, A000204, A001606.

cp's OEIS Frontend

A216575 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 10*b^2.

Views

Author

Keywords

Links

Crossrefs

A290246 Prime numbers that are common indices to both prime Lucas and prime Wagstaff numbers.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A330777 Numbers k such that k and Lucas(k) have the same number of divisors.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A377183 Positive numbers k such that L(k)-1 is prime, where L(k) is the k-th Lucas number.

Views

Author

Keywords

Comments

Examples

Crossrefs

A377184 Numbers k such that L(k)+1 is prime, where L(k) is the k-th Lucas number.

Views

Author

Keywords

Comments

Examples

Crossrefs