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 1-10 of 31 results. Next

A100683 a(n) = a(n-1) + a(n-2) + a(n-3); a(0) = -1, a(1) = 2, a(2) = 2.

Original entry on oeis.org

-1, 2, 2, 3, 7, 12, 22, 41, 75, 138, 254, 467, 859, 1580, 2906, 5345, 9831, 18082, 33258, 61171, 112511, 206940, 380622, 700073, 1287635, 2368330, 4356038, 8012003, 14736371, 27104412, 49852786, 91693569, 168650767, 310197122
Offset: 0

Views

Author

N. J. A. Sloane, Dec 08 2004

Keywords

Comments

A tribonacci sequence.
From Greg Dresden and Veda Garigipati, Jun 14 2022: (Start)
For n >= 2, a(n+2) is the number of ways to tile this figure of length n with squares, dominoes, and "trominoes" (of length 3):
_
|||___________
|||_|||_|||
As an example, here is one of the 254 possible tilings of this figure of length 8 with squares, dominoes, and trominoes:
_
| ||__________
||____|_|_|_|. (End)

Links

Crossrefs

Cf. A232542, A232543.
Cf. A001590, A020992.
Cf. A000073.

Programs

  • Maple
    a[0]:=-1:a[1]:=2:a[2]:=2:for n from 3 to 42 do a[n]:=a[n-1]+a[n-2]+a[n-3] od: seq(a[n],n=0..42);
  • Mathematica
    a[0] = -1; a[1] = a[2] = 2; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3]; Table[ a[n], {n, 0, 35}] (* Robert G. Wilson v, Dec 09 2004 *)
LinearRecurrence[{1,1,1},{-1,2,2},34] (* Ray Chandler, Dec 08 2013 *)
  • PARI
    Vec(-(1-3*x-x^2)/(1-x-x^2-x^3) + O(x^70)) \\ Michel Marcus, Sep 25 2015

Formula

a(n+1) = 2*A001590(n+1) + A020992(n). - Creighton Dement, May 02 2005
O.g.f.: -(1-3x-x^2)/(1-x-x^2-x^3). - R. J. Mathar, Aug 22 2008
a(n) = T(n-2) + T(n) + T(n+1) where T(n) = A000073(n) the tribonacci sequence, for n >= 2. - Greg Dresden and Veda Garigipati, Jun 14 2022

Extensions

More terms from Emeric Deutsch, Farideh Firoozbakht and Robert G. Wilson v, Dec 08 2004

A235862 Indices of primes in A141523.

Original entry on oeis.org

0, 3, 4, 5, 8, 10, 14, 16, 24, 30, 40, 54, 63, 66, 67, 109, 188, 203, 421, 463, 704, 730, 798, 1155, 1259, 1376, 1789, 2095, 2650, 3833, 4538, 4794, 4840, 5386, 8348, 15176, 17282, 21250, 21386, 21825, 31242, 32843, 33706, 37026, 47546, 66848
Offset: 1

Views

Author

Robert Price, Jan 16 2014

Keywords

Comments

a(47) > 2*10^5.

Links

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523.

Programs

  • Mathematica
    a={3,1,1}; Print[0]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]

Extensions

Name clarified by Arthur O'Dwyer, Jul 25 2024

A232543 Indices of primes in A100683.

Original entry on oeis.org

1, 2, 3, 4, 7, 11, 12, 27, 32, 119, 127, 136, 611, 755, 872, 1676, 5363, 15623, 27564, 42679, 54576, 74123, 91043, 104331
Offset: 1

Views

Author

Robert Price, Nov 25 2013

Keywords

Comments

a(25) > 2*10^5.

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232542.

Programs

  • Mathematica
    a={-1,2,2};Print[1],Print[2];For[n=3,n<=1000,n++,sum=Plus@@a;If[PrimeQ[sum],Print[n]];a=RotateLeft[a]; a[[3]]=sum]

Formula

A100683(a(n)) = A232542(n). - Arthur O'Dwyer, 25 Jul 2024

Extensions

Name clarified by Arthur O'Dwyer, Jul 25 2024

A233554 Indices of primes in the tribonacci-like sequence, A020992.

Original entry on oeis.org

1, 3, 6, 15, 19, 22, 207, 542, 2374, 10579, 17726, 43182
Offset: 1

Views

Author

Robert Price, Dec 12 2013

Keywords

Comments

a(13) > 2*10^5.

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498.

Programs

  • Mathematica
    a={0,2,1};Print[1];For[n=3,n<=1000,n++,sum=Plus@@a;If[PrimeQ[sum],Print[n]];a=RotateLeft[a]; a[[3]]=sum]

A234696 Indices of primes in the tribonacci-like sequence, A214727.

Original entry on oeis.org

1, 2, 3, 8, 16, 20, 64, 208, 364, 2652, 7763, 17280, 24104, 31823, 70864, 74008
Offset: 1

Views

Author

Robert Price, Dec 29 2013

Keywords

Comments

a(17) > 2*10^5.

Links

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727.

Programs

  • Mathematica
    a={1, 2, 2}; Print[2]; Print[2]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]
Position[LinearRecurrence[{1,1,1},{1,2,2},75000],?PrimeQ]-1//Flatten (* _Harvey P. Dale, Sep 02 2016 *)

A247027 Indices of primes in the tetranacci sequence A001631.

Original entry on oeis.org

5, 7, 12, 19, 47, 97, 124, 244, 564, 1037, 12007, 13662, 180039
Offset: 1

Views

Author

Robert Price, Sep 09 2014

Keywords

Comments

a(14) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523,A214825, A235862.

Programs

  • Mathematica
    a={0,0,1,0}; For[n=4, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[4]]=sum]

A241660 Indices of primes in A001630.

Original entry on oeis.org

3, 4, 7, 19, 62, 94, 722, 5197, 5262, 6182, 14007, 21579, 35354, 75592
Offset: 1

Views

Author

Robert Price, Apr 26 2014

Keywords

Comments

a(15) > 2*10^5.

Links

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523,A214825, A235862.

Programs

  • Mathematica
    a={0,0,1,2}; Print[3]; For[n=4, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[4]]=sum]

Extensions

Prepended a(1)=3 and Mathematica program corrected by Robert Price, Sep 09 2014

A243622 Indices of primes in A214829.

Original entry on oeis.org

1, 2, 4, 10, 11, 12, 13, 58, 63, 89, 132, 157, 426, 457, 506, 613, 1839, 1936, 2042, 2355, 3178, 3782, 8556, 8688, 22152, 23232, 44074, 71770, 222666
Offset: 1

Views

Author

Robert Price, Jun 07 2014

Keywords

Comments

a(30) > 222666.

Links

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523,A214825, A235862, A214827, A214828.

Programs

  • Mathematica
    a={1,7,7}; Print["1"]; Print["2"]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]

Extensions

a(27) corrected by Robert Price, May 22 2019
a(29) from Robert Price, May 23 2019

A242324 Indices of primes in the tribonacci-like sequence A214827.

Original entry on oeis.org

1, 2, 3, 5, 7, 8, 11, 13, 14, 15, 18, 39, 42, 46, 128, 319, 501, 645, 749, 785, 924, 1786, 1810, 3032, 3053, 3913, 4444, 5611, 6290, 20526, 20850, 23431, 44281, 45981, 103816, 133938
Offset: 1

Views

Author

Robert Price, May 10 2014

Keywords

Comments

a(37) > 2*10^5.

Links

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523,A214825, A235862, A214827.

Programs

  • Mathematica
    a={1,5,5}; Print[1];Print[2]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]

A247561 Indices of primes in the tetranacci sequence A000288.

Original entry on oeis.org

5, 6, 10, 11, 12, 13, 18, 30, 31, 36, 38, 97, 108, 150, 196, 221, 277, 532, 596, 2468, 2691, 3773, 4303, 5755, 8925, 10083, 11708, 14080, 19990, 24102, 34767, 35973, 39238, 49760, 97706
Offset: 1

Views

Author

Robert Price, Sep 27 2014

Keywords

Comments

a(36) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288.

Programs

  • Mathematica
    a={1,1,1,1}; For[n=4, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[4]]=sum]
Flatten[Position[LinearRecurrence[{1,1,1,1},{1,1,1,1},10^5], ?PrimeQ]]- 1 (* _Harvey P. Dale, Dec 20 2016 *)
Showing 1-10 of 31 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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