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 22 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

A232542 Primes in A100683.

Original entry on oeis.org

2, 2, 3, 7, 41, 467, 859, 8012003, 168650767, 17843905055671832482869722050793, 2337143892123435886770270228393473, 563028582965218666043722998152482699
Offset: 1

Views

Author

Robert Price, Nov 25 2013

Keywords

Crossrefs

Cf. A001590, A100683, A231574, A231575, A232543.

Programs

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

Extensions

Name clarified by Arthur O'Dwyer, Jul 25 2024

A230607 Primes in the tribonacci-like sequence A214899.

Original entry on oeis.org

2, 2, 5, 173, 1979, 10035601, 1314434453, 15043078019, 75946890143515970461691, 9947307490759622919990767, 33651500197152003774080593, 113842209720657202395344053, 577291982170349695261586984393, 33503139717732963900675717496847941
Offset: 1

Views

Author

Robert Price, Dec 05 2013

Keywords

Crossrefs

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

Programs

  • Mathematica
    a={2,1,2}; Print[2]; Print[2]; 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},{2,1,2},300],PrimeQ] (* Harvey P. Dale, Jul 30 2015 *)

Extensions

More terms from Harvey P. Dale, Jul 30 2015

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]
Showing 1-10 of 22 results. Next

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

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