A001606 -id:A001606 - cp's OEIS frontend

A216554 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 3*b^2.

2, 4, 11, 17, 19, 41, 113, 313, 353, 617, 1097, 1361, 4787, 4793, 5851, 8467, 10691, 12251, 13963, 14449, 35449, 36779, 44507, 51169, 56003, 89849, 140057, 148091, 159521, 183089, 193201, 202667, 387433, 443609, 574219, 616787, 692147

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

Select[Range[693000],PrimeQ[LucasL[#]]&&Length[Solve[{a^2+3b^2==LucasL[#],a>=0,b>=0},{a,b},Integers]]>0&] (* Harvey P. Dale, Apr 19 2020 *)

A216555 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + 3*b^2.

Original entry on oeis.org

0, 5, 7, 8, 13, 16, 31, 37, 47, 53, 61, 71, 79, 503, 613, 863, 7741, 19469, 81671, 94823, 344293, 532277, 631181, 637751, 651821

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

A216562 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 2*b^2.

Original entry on oeis.org

0, 4, 5, 11, 13, 16, 17, 37, 41, 47, 53, 61, 71, 113, 313, 353, 503, 613, 617, 863, 1097, 1361, 4787, 4793, 7741, 10691, 12251, 14449, 19469, 35449, 36779, 44507, 51169, 56003, 81671, 89849, 94823, 140057, 148091, 159521, 183089, 193201, 202667, 344293, 387433, 443609, 532277, 616787, 631181, 637751, 651821, 692147

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

A216563 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 5*b^2.

Original entry on oeis.org

4, 13, 31, 61, 313, 613, 5851, 7741, 13963, 193201, 344293, 387433

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

A216564 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + 2*b^2.

Original entry on oeis.org

7, 19, 31, 79, 5851, 8467, 13963, 574219

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

A216565 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + 5*b^2.

Original entry on oeis.org

0, 2, 5, 7, 8, 11, 16, 17, 19, 37, 41, 47, 53, 71, 79, 113, 353, 503, 617, 863, 1097, 1361, 4787, 4793, 8467, 10691, 12251, 14449, 19469, 35449, 36779, 44507, 51169, 56003, 81671, 89849, 94823, 140057, 148091, 159521, 183089, 202667, 443609, 532277, 574219, 616787, 631181, 637751, 651821, 692147

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

A216566 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + b^2.

Original entry on oeis.org

2, 4, 5, 8, 11, 16, 17, 41, 47, 53, 71, 113, 353, 503, 617, 863, 1097, 1361, 4787, 4793, 10691, 12251, 19469, 36779, 44507, 56003, 81671, 89849, 94823, 140057, 148091, 159521, 183089, 202667, 443609, 532277, 616787, 631181, 637751, 651821, 692147

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

A216567 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + b^2.

Original entry on oeis.org

0, 7, 13, 19, 31, 37, 61, 79, 313, 613, 5851, 7741, 8467, 13963, 14449, 35449, 51169, 193201, 344293, 387433, 574219

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

A216571 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 6*b^2.

Original entry on oeis.org

4, 11, 313, 4787, 10691, 12251, 14449, 35449, 36779, 44507, 51169, 56003, 148091, 193201, 202667, 387433, 616787, 692147

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

A216572 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + 6*b^2.

Original entry on oeis.org

0, 2, 5, 7, 8, 13, 16, 17, 19, 31, 37, 41, 47, 53, 61, 71, 79, 113, 353, 503, 613, 617, 863, 1097, 1361, 4793, 5851, 7741, 8467, 13963, 19469, 81671, 89849, 94823, 140057, 159521, 183089, 344293, 443609, 532277, 574219, 631181, 637751, 651821

Offset: 1

V. Raman, Sep 08 2012

nonn

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Cf. A000032, A001606.

cp's OEIS Frontend

A216554 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 3*b^2.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A216555 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + 3*b^2.

Views

Author

Keywords

Links

Crossrefs

A216562 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 2*b^2.

Views

Author

Keywords

Links

Crossrefs

A216563 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 5*b^2.

Views

Author

Keywords

Links

Crossrefs

A216564 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + 2*b^2.

Views

Author

Keywords

Links

Crossrefs

A216565 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + 5*b^2.

Views

Author

Keywords

Links

Crossrefs

A216566 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + b^2.

Views

Author

Keywords

Links

Crossrefs

A216567 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + b^2.

Views

Author

Keywords

Links

Crossrefs

A216571 Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 6*b^2.

Views

Author

Keywords

Links

Crossrefs

A216572 Numbers n such that the n-th Lucas number is prime, but cannot be written in the form a^2 + 6*b^2.

Views

Author

Keywords

Links

Crossrefs