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 29 results. Next

A020992 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 0, a(1) = 2, a(2) = 1.

Original entry on oeis.org

0, 2, 1, 3, 6, 10, 19, 35, 64, 118, 217, 399, 734, 1350, 2483, 4567, 8400, 15450, 28417, 52267, 96134, 176818, 325219, 598171, 1100208, 2023598, 3721977, 6845783, 12591358, 23159118, 42596259, 78346735, 144102112, 265045106, 487493953, 896641171, 1649180230
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Tribonacci sequence beginning 0, 2, 1.
Pisano period lengths: 1, 4, 13, 8, 31, 52, 48, 16, 39, 124, 110, 104, 168, 48, 403, 32, 96, 156, 360, 248,.... - R. J. Mathar, Aug 10 2012
One bisection is 0, 1, 6, 19, 64, 217, 734, 2483, 8400,.. and the other 2, 3, 10, 35, 118, 399, 1350, 4567,... both with recurrence b(n)=3*b(n-1)+b(n-2)+b(n-3). - R. J. Mathar, Aug 10 2012
From Greg Dresden and Jiarui Zhou, Jun 30 2025: (Start)
For n >= 4, 2*a(n) is the number of ways to tile this shape of length n-2 with squares, dominos, and trominos (of length 3):
._
|||___________
|||_|||_|||
|_|.
As an example, here is one of the 2*a(10) = 434 ways to tile this shape of length 8:
._
| ||__________
| |_|_____|||
|_| (End)

Links

Crossrefs

Cf. A000032, A000073, A001590, A232498, A233554.

Programs

  • Magma
    I:=[0,2,1]; [n le 3 select I[n] else Self(n-1) + Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Feb 09 2018
  • Mathematica
    LinearRecurrence[{1,1,1},{0,2,1},100] (* Vladimir Joseph Stephan Orlovsky, Jun 07 2011 *)
  • PARI
    my(x='x+O('x^30)); concat([0], Vec(x*(2-x)/(1-x-x^2-x^3))) \\ G. C. Greubel, Feb 09 2018

Formula

G.f.: x*(2-x)/(1-x-x^2-x^3).
a(n) = 2*A000073(n+1)-A000073(n). - R. J. Mathar, Aug 22 2008
a(n) = 2*a(n-1) - a(n-4), n>3. - Vincenzo Librandi, Jun 08 2011

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

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 *)

A247192 Indices of primes in the hexanacci numbers sequence A000383.

Original entry on oeis.org

7, 9, 30, 31, 33, 46, 52, 54, 82, 102, 109, 124, 210, 301, 351, 365, 369, 1045, 2044, 2125, 2143, 2815, 4377, 4754, 4893, 7310, 11558, 17602, 17929, 28389, 32100, 44298, 106725, 151678, 197953
Offset: 1

Views

Author

Robert Price, Dec 03 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, A000322, A000383, A249413.

Programs

  • Mathematica
    a={1,1,1,1,1}; For[n=5, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[5]]=sum]
Showing 1-10 of 29 results. Next

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

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