A258085 -id:A258085 - cp's OEIS frontend

A259623 Strictly increasing list of F and F + 1, where F = A000045, the Fibonacci numbers.

1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 21, 22, 34, 35, 55, 56, 89, 90, 144, 145, 233, 234, 377, 378, 610, 611, 987, 988, 1597, 1598, 2584, 2585, 4181, 4182, 6765, 6766, 10946, 10947, 17711, 17712, 28657, 28658, 46368, 46369, 75025, 75026, 121393, 121394, 196418

Offset: 1

Clark Kimberling and Peter J. C. Moses, Jul 01 2015

Clark Kimberling, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (0, 2, 0, 0, 0, -1).

Cf. A000045, A258085.

Mathematica
```
Union[#, # + 1] &[Fibonacci[Range[50]]]
```

G.f.: -((-1 - 2 x - x^2 + x^4 + 2 x^5 + x^6 + x^7)/((-1 + x) (1 + x) (-1 + x^2 + x^4))).

A259624 Strictly increasing list of F - 1, F, and F + 1, where F = A000045, the Fibonacci numbers.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 20, 21, 22, 33, 34, 35, 54, 55, 56, 88, 89, 90, 143, 144, 145, 232, 233, 234, 376, 377, 378, 609, 610, 611, 986, 987, 988, 1596, 1597, 1598, 2583, 2584, 2585, 4180, 4181, 4182, 6764, 6765, 6766, 10945, 10946, 10947

Offset: 1

Clark Kimberling and Peter J. C. Moses, Jul 01 2015

Clark Kimberling, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (-1, -1, 1, 1, 1, 1, 1, 1).

Cf. A000045, A258085, A259623.

Union[# - 1, #, # + 1] &[Fibonacci[Range[50]]]
CoefficientList[Series[-((x (1+x) (1+x+x^2+x^4) (1+x+2 x^2+x^3+x^4+x^5))/((1+x+x^2) (-1+x^3+x^6))),{x,0,60}],x] (* or *) LinearRecurrence[{-1,-1,1,1,1,1,1,1},{0,1,2,3,4,5,6,7,8,9,12,13},60] (* Harvey P. Dale, Nov 21 2024 *)

G.f.: -((x (1 + x) (1 + x + x^2 + x^4) (1 + x + 2 x^2 + x^3 + x^4 + x^5))/((1 + x + x^2) (-1 + x^3 + x^6))).

A259626 List of numbers L and L + 1, where L = A000032, the Lucas numbers, sorted into increasing order and duplicates removed.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 11, 12, 18, 19, 29, 30, 47, 48, 76, 77, 123, 124, 199, 200, 322, 323, 521, 522, 843, 844, 1364, 1365, 2207, 2208, 3571, 3572, 5778, 5779, 9349, 9350, 15127, 15128, 24476, 24477, 39603, 39604, 64079, 64080, 103682, 103683, 167761, 167762

Offset: 1

Clark Kimberling and Peter J. C. Moses, Jul 01 2015

Clark Kimberling, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (0, 2, 0, 0, 0, -1).

Cf. A000032, A258085, A259623, A259624, A259625, A259627.

Mathematica
```
Union[#, # + 1] &[LucasL[Range[50]]]
```

G.f.: -((-1 - 2 x - x^2 + x^4 + x^5 + x^6 + x^7 + x^8)/((-1 + x) (1 + x) (-1 + x^2 + x^4)))

A259627 List of numbers L - 1, L, and L+1, where L = A000032, the Lucas numbers, sorted into increasing order and duplicates removed.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 17, 18, 19, 28, 29, 30, 46, 47, 48, 75, 76, 77, 122, 123, 124, 198, 199, 200, 321, 322, 323, 520, 521, 522, 842, 843, 844, 1363, 1364, 1365, 2206, 2207, 2208, 3570, 3571, 3572, 5777, 5778, 5779, 9348, 9349, 9350, 15126

Offset: 1

Clark Kimberling and Peter J. C. Moses, Jul 01 2015

Clark Kimberling, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (-1, -1, 1, 1, 1, 1, 1, 1).

Cf. A000032, A258085, A259623-A259626.

Union[# - 1, #, # + 1] &[LucasL[Range[50]]]

G.f.: -((x (1 + x) (1 + x^2) (1 + 2 x + 3 x^2 + 2 x^3 + 2 x^4 + 2 x^5 +

2 x^6))/((1 + x + x^2) (-1 + x^3 + x^6)))

A259625 List of numbers L - 1 and L, where L = A000032, the Lucas numbers, sorted into increasing order and duplicates removed.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 10, 11, 17, 18, 28, 29, 46, 47, 75, 76, 122, 123, 198, 199, 321, 322, 520, 521, 842, 843, 1363, 1364, 2206, 2207, 3570, 3571, 5777, 5778, 9348, 9349, 15126, 15127, 24475, 24476, 39602, 39603, 64078, 64079, 103681, 103682, 167760, 167761

Offset: 1

Clark Kimberling and Peter J. C. Moses, Jul 01 2015

Clark Kimberling, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (0, 2, 0, 0, 0, -1).

Cf. A000032, A258085, A259623, A259624, A259626, A259627.

Mathematica
```
Union[#, # - 1] &[LucasL[Range[50]]]
```

G.f.: -((x (-1 - 2 x - x^2 + x^5 + x^6 + x^7))/((-1 + x) (1 + x) (-1 + x^2 + x^4)))

cp's OEIS Frontend

A259623 Strictly increasing list of F and F + 1, where F = A000045, the Fibonacci numbers.

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A259624 Strictly increasing list of F - 1, F, and F + 1, where F = A000045, the Fibonacci numbers.

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Mathematica

Formula

A259626 List of numbers L and L + 1, where L = A000032, the Lucas numbers, sorted into increasing order and duplicates removed.

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Mathematica

Formula

A259627 List of numbers L - 1, L, and L+1, where L = A000032, the Lucas numbers, sorted into increasing order and duplicates removed.

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Links

Crossrefs

Programs

Mathematica

Formula

A259625 List of numbers L - 1 and L, where L = A000032, the Lucas numbers, sorted into increasing order and duplicates removed.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula