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 20 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

A232498 Primes in the tribonacci-like sequence, A020992.

Original entry on oeis.org

2, 3, 19, 4567, 52267, 325219, 2967036956187340614662532876709507060271690954641131383
Offset: 1

Views

Author

Robert Price, Dec 12 2013

Keywords

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232543, A214899, A020992, A233554.

Programs

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

A235873 Primes in the tribonacci-like sequence, A141523.

Original entry on oeis.org

3, 5, 7, 13, 83, 281, 3217, 10883, 1425427, 55187617, 24453221203, 124001884480009, 29872617402415741, 185875267730565697, 341877918058715653, 44580781450601596678810171573, 36012536557658790037420884825332617431175065740791
Offset: 1

Views

Author

Robert Price, Jan 16 2014

Keywords

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232543, A214899, A020992, A233554. A214727, A234696, A141523, A235862.

Programs

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

A249413 Primes in the hexanacci numbers sequence A000383.

Original entry on oeis.org

11, 41, 72426721, 143664401, 565262081, 4160105226881, 253399862985121, 997027328131841, 212479323351825962211841, 188939838859312612896128881921, 22828424707602602744356458636161, 661045104283639247572028952777478721
Offset: 1

Views

Author

Robert Price, Dec 03 2014

Keywords

Comments

a(13) is too large to display here. It has 62 digits and is the 210th term in A000383.

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192.

Programs

  • Mathematica
    a={1,1,1,1,1,1}; For[n=6, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[5]]=sum]

A242576 Prime terms in A214828.

Original entry on oeis.org

13, 151, 277, 36313, 225949, 7129366889, 933784181621, 19397107178326126131136629644898891137047, 401151570474397232184569825031979125080583558010764826781295643008140597581801
Offset: 1

Views

Author

Robert Price, May 17 2014

Keywords

Comments

a(10) has 119 digits and thus is too large to display here. It corresponds to A214828(448).

Links

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232543, A214899, A020992, A233554. A214727, A234696, A141523, A235862, A214825, A235873, A242324, A214827, A214828.

Programs

  • Mathematica
    a={1,6,6}; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[3]]=sum]
Select[LinearRecurrence[{1,1,1},{1,6,6},350],PrimeQ] (* Harvey P. Dale, Jul 21 2018 *)
  • PARI
    my(x='x+O('x^500)); select(isprime, Vec((1+5*x-x^2)/(1-x-x^2-x^3))) \\ Michel Marcus, Jun 16 2025

A243623 Prime terms in A214829.

Original entry on oeis.org

7, 29, 1087, 1999, 3677, 6763, 5487349608898607, 115507410616162687, 878001744429057971864287, 210582098197038415344728317608265501, 870277059555114378903885645581650740066907
Offset: 1

Views

Author

Robert Price, Jun 07 2014

Keywords

Comments

a(12) has 114 digits and thus is too large to display here. It corresponds to A214829(426).

Links

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232543, A214899, A020992, A233554. A214727, A234696, A141523, A235862,A214825, A235873, A214827, A242324, A214827, A214828, A214829, A242572, A242576, A243622.

Programs

  • Maple
    f:= gfun:-rectoproc({a(n) = a(n-1) + a(n-2) + a(n-3), a(0) = 1, a(1) = 7, a(2) = 7},a(n),remember):
select(isprime, map(f, [$2..1000])); # Robert Israel, Sep 02 2024
  • Mathematica
    a={1,7,7}; Print["7"]; Print["7"]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[3]]=sum]

Extensions

7 inserted as a(1) by Robert Israel, Sep 02 2024

A246518 Prime terms in A141036.

Original entry on oeis.org

2, 11, 2713, 4066709, 289593761, 30236674150891013353640837416685668536004108580572237299601, 45323907186142905348893078704293178796516046414129798590935901
Offset: 1

Views

Author

Robert Price, Aug 28 2014

Keywords

Comments

a(8) has 91 digits and thus is too large to display here. It corresponds to A141036(482).
a(n) = A141036(A246517(n)).

Links

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232543, A214899, A020992, A233554. A214727, A234696, A141523, A235862, A214825, A235873, A242324, A214827-A214829, A242572, A242576, A243622, A244001, A214831, A244002, A141036, A246517.
Cf. A010051.

Programs

  • Haskell
    a246518 n = a246518_list !! (n-1)
a246518_list = filter ((== 1) . a010051'') $ a141036_list
-- Reinhard Zumkeller, Sep 15 2014
  • Mathematica
    a={2,1,1}; Print[2]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[3]]=sum]

A244002 Prime terms in A214830.

Original entry on oeis.org

17, 199, 2273, 547609, 71724269, 131339891338466303, 31640376596545867021, 2253137772896035203743
Offset: 1

Views

Author

Robert Price, Jun 17 2014

Keywords

Comments

a(10) has 182 digits and thus is too large to display here. It corresponds to A214830(688).

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232543, A214899, A020992, A233554. A214727, A234696, A141523, A235862,A214825, A235873, A214827, A242324, A214827, A214828, A214829, A242572, A242576, A243622, A214829, A244001.

Programs

  • Mathematica
    a={1,8,8}; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[3]]=sum]

A253333 Primes in the 7th-order Fibonacci numbers A060455.

Original entry on oeis.org

7, 13, 97, 193, 769, 1531, 3049, 6073, 12097, 24097, 95617, 379399, 2998753, 187339729, 373174033, 2949551617, 184265983633, 731152932481, 88025699967469825543, 175344042716296888429, 4979552865927484193343796114081304399449
Offset: 1

Views

Author

Robert Price, Dec 30 2014

Keywords

Comments

a(22) is too large to display here. It has 53 digits and is the 180th term in A060455.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192, A060455, A253318.

Programs

  • Mathematica
    a={1,1,1,1,1,1,1}; step=7; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,sum]]; a=RotateLeft[a]; a[[7]]=sum]; lst
With[{c=PadRight[{},7,1]},Select[LinearRecurrence[c,c,150],PrimeQ]] (* Harvey P. Dale, May 08 2015 *)
  • PARI
    lista(nn) = {gf = ( -1+x^2+2*x^3+3*x^4+4*x^5+5*x^6 ) / ( -1+x+x^2+x^3+x^4+x^5+x^6+x^7 ); for (n=0, nn, if (isprime(p=polcoeff(gf+O(x^(n+1)), n)), print1(p, ", ")););} \\ Michel Marcus, Jan 11 2015

A254413 Primes in the 8th-order Fibonacci numbers A123526.

Original entry on oeis.org

29, 113, 449, 226241, 14307889, 113783041, 1820091580429249, 233322881089059894782836851617, 29566627412209231076314948970028097, 59243719929958343565697204780596496129, 7507351981539044730893385057192143660843521
Offset: 1

Views

Author

Robert Price, Jan 30 2015

Keywords

Comments

a(12) is too large to display here. It has 46 digits and is the 158th term in A123526.

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192, A060455, A253318, A079262, A253705, A123526, A254412.

Programs

  • Mathematica
    a={1,1,1,1,1,1,1,1}; step=8; lst={}; For[n=step+1,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,sum]]; a=RotateLeft[a]; a[[step]]=sum]; lst
Select[With[{lr=PadRight[{},8,1]},LinearRecurrence[lr,lr,200]],PrimeQ] (* Harvey P. Dale, Dec 03 2022 *)
Showing 1-10 of 20 results. Next

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

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