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.

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A214829 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 7.

Original entry on oeis.org

1, 7, 7, 15, 29, 51, 95, 175, 321, 591, 1087, 1999, 3677, 6763, 12439, 22879, 42081, 77399, 142359, 261839, 481597, 885795, 1629231, 2996623, 5511649, 10137503, 18645775, 34294927, 63078205, 116018907, 213392039, 392489151, 721900097, 1327781287, 2442170535
Offset: 0

Views

Author

Abel Amene, Aug 07 2012

Keywords

Comments

See comments in A214727.

Links

Crossrefs

Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825, A214826, A214827, A214828, A214830, A214831.

Programs

  • GAP
    a:=[1,7,7];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 24 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+6*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019
  • Mathematica
    LinearRecurrence[{1,1,1}, {1,7,7}, 40] (* G. C. Greubel, Apr 24 2019 *)
  • PARI
    Vec((x^2-6*x-1)/(x^3+x^2+x-1) + O(x^40)) \\ Michel Marcus, Jun 04 2017
  • Sage
    ((1+6*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019

Formula

G.f.: (1+6*x-x^2)/(1-x-x^2-x^3).
a(n) = -A000073(n) + 6*A000073(n+1) + A000073(n+2). - G. C. Greubel, Apr 24 2019

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 *)

A214826 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 4.

Original entry on oeis.org

1, 4, 4, 9, 17, 30, 56, 103, 189, 348, 640, 1177, 2165, 3982, 7324, 13471, 24777, 45572, 83820, 154169, 283561, 521550, 959280, 1764391, 3245221, 5968892, 10978504, 20192617, 37140013, 68311134, 125643764, 231094911, 425049809
Offset: 0

Views

Author

Abel Amene, Jul 29 2012

Keywords

Comments

See Comments in A214727.

Links

Crossrefs

Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831.

Programs

  • GAP
    a:=[1,4,4];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 23 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+3*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 23 2019
  • Mathematica
    LinearRecurrence[{1,1,1},{1,4,4},33] (* Ray Chandler, Dec 08 2013 *)
  • PARI
    my(x='x+O('x^40)); Vec((1+3*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019
  • Sage
    ((1+3*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019

Formula

G.f.: (1+3*x-x^2)/(1-x-x^2-x^3).
a(n) = K(n) - 2*T(n+1) + 5*T(n), where K(n) = A001644(n) and T(n) = A000073(n+1). - G. C. Greubel, Apr 23 2019

A214830 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 8.

Original entry on oeis.org

1, 8, 8, 17, 33, 58, 108, 199, 365, 672, 1236, 2273, 4181, 7690, 14144, 26015, 47849, 88008, 161872, 297729, 547609, 1007210, 1852548, 3407367, 6267125, 11527040, 21201532, 38995697, 71724269, 131921498, 242641464, 446287231, 820850193, 1509778888
Offset: 0

Views

Author

Abel Amene, Aug 07 2012

Keywords

Comments

See comments in A214727.

Links

Crossrefs

Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831.

Programs

  • GAP
    a:=[1,8,8];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 24 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+7*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019
  • Mathematica
    CoefficientList[Series[(x^2-7*x-1)/(x^3+x^2+x-1), {x, 0, 40}], x] (* Wesley Ivan Hurt, Jun 18 2014 *)
LinearRecurrence[{1,1,1}, {1,8,8}, 40] (* G. C. Greubel, Apr 24 2019 *)
  • PARI
    my(x='x+O('x^40)); Vec((1+7*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 24 2019
  • Sage
    ((1+7*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019

Formula

G.f.: (1+7*x-x^2)/(1-x-x^2-x^3).
a(n) = -A000073(n) + 7*A000073(n+1) + A000073(n+2). - G. C. Greubel, Apr 24 2019

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
Previous Showing 11-20 of 54 results. Next

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

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