A214828 -id:A214828 - cp's OEIS frontend

A242576 Prime terms in A214828.

13, 151, 277, 36313, 225949, 7129366889, 933784181621, 19397107178326126131136629644898891137047, 401151570474397232184569825031979125080583558010764826781295643008140597581801

Offset: 1

Robert Price, May 17 2014

nonn

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

Michel Marcus, Table of n, a(n) for n = 1..17

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

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 *)

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

A242572 Indices of primes in A214828.

Original entry on oeis.org

3, 7, 8, 16, 19, 36, 44, 151, 292, 448, 467, 896, 1148, 1607, 1711, 1956, 2020, 6635, 14228, 25519, 43140, 74984, 77696, 137975

Offset: 1

Robert Price, May 17 2014

a(25) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

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

a={1,6,6}; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]

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

Abel Amene, Aug 07 2012

See comments in A214727.

Robert Price, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1).

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

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

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+6*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019

LinearRecurrence[{1,1,1}, {1,7,7}, 40] (* G. C. Greubel, Apr 24 2019 *)

Vec((x^2-6*x-1)/(x^3+x^2+x-1) + O(x^40)) \\ Michel Marcus, Jun 04 2017

((1+6*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019

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

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

Robert Price, Jun 07 2014

a(30) > 222666.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

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

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]

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

a(29) from Robert Price, May 23 2019

A243623 Prime terms in A214829.

Original entry on oeis.org

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

Offset: 1

Robert Price, Jun 07 2014

nonn

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

Robert Israel, Table of n, a(n) for n = 1..20

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

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

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]

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

A244001 Indices of primes in A214830.

Original entry on oeis.org

3, 7, 11, 20, 28, 63, 72, 79, 688, 795, 999, 2716, 13220, 15940, 17903, 26832, 28416, 33448, 117923

Offset: 1

Robert Price, Jun 17 2014

a(20) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523,A214825, A235862, A214827, A214828, A214829, A243622, A243623.

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

Robert Price, Jun 17 2014

nonn

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

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.

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

A244930 Indices of primes in A214831.

Original entry on oeis.org

3, 4, 7, 8, 16, 26, 34, 42, 78, 94, 101, 107, 216, 255, 543, 562, 851, 981, 1099, 1528, 1824, 1955, 2122, 2488, 2500, 15331, 15961, 24107, 24938, 26051, 58504, 61617, 81034, 85119, 89768, 90597, 97191, 116899, 195346

Offset: 1

Robert Price, Jul 08 2014

nonn

a(40) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A214827, A214828, A214829, A243622, A243623, A214831.

a={1,9,9}; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]
Flatten[Position[LinearRecurrence[{1,1,1},{1,9,9},200000],?PrimeQ]]-1 (* The prime number at index 195346 (term a(39) of this sequence) has 51699 digits, so this program takes a long time to run. *) (* _Harvey P. Dale, Dec 29 2019 *)

A244931 Prime terms in A214831.

Original entry on oeis.org

19, 37, 223, 409, 53617, 23757289, 3111662089, 407556643177, 1372675688565303822697, 23548271681390871672120649, 1676892190264006259992141409, 64923481849284379431377700019

Offset: 1

Robert Price, Jul 08 2014

nonn

a(13) has 58 digits and thus is too large to display here. It corresponds to A214831(216).

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, A214831, A244002.

a={1,9,9}; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[3]]=sum]

A268410 a(n) = a(n - 1) + a(n - 2) + a(n - 3) for n>2, a(0)=5, a(1)=7, a(2)=9.

Original entry on oeis.org

5, 7, 9, 21, 37, 67, 125, 229, 421, 775, 1425, 2621, 4821, 8867, 16309, 29997, 55173, 101479, 186649, 343301, 631429, 1161379, 2136109, 3928917, 7226405, 13291431, 24446753, 44964589, 82702773, 152114115, 279781477, 514598365, 946493957

Offset: 0

Ilya Gutkovskiy, Feb 04 2016

Tribonacci sequence beginning 5, 7, 9.

In general, the ordinary generating function for the recurrence relation b(n) = b(n-1) + b(n-2) + b(n-3), with n>2 and b(0)=k, b(1)=m, b(2)=q, is (k + (m-k)*x + (q-m-k)*x^2)/(1 - x - x^2 - x^3).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Tribonacci Number
Index entries for linear recurrences with constant coefficients, signature (1,1,1)

Cf. similar sequences with initial values (p,q,r): A000073 (0,0,1), A081172 (1,1,0), A001590 (0,1,0; also 1,2,3), A214899 (2,1,2), A001644 (3,1,3), A145027 (2,3,4), A000213 (1,1,1), A141036 (2,1,1), A141523 (3,1,1), A214727 (1,2,2), A214825 (1,3,3), A214826 (1,4,4), A214827 (1,5,5), A214828 (1,6,6), A214829 (1,7,7), A214830 (1,8,8), A214831 (1,9,9).

a:=[5,7,9];; 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

I:=[5,7,9]; [n le 3 select I[n] else Self(n-1)+Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 04 2016

LinearRecurrence[{1, 1, 1}, {5, 7, 9}, 40]
RecurrenceTable[{a[0]==5, a[1]==7, a[2]==9, a[n]==a[n-1]+a[n-2]+a[n-3]}, a, {n, 40}]

my(x='x+O('x^40)); Vec((5+2*x-3*x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019

((5+2*x-3*x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019

G.f.: (5 + 2*x - 3*x^2)/(1 - x - x^2 - x^3).

a(n) = 3*K(n) - 4*T(n+1) + 8*T(n), where K(n) = A001644(n) and T(n) =A000073(n+1). - G. C. Greubel, Apr 23 2019

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A242576 Prime terms in A214828.

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A242572 Indices of primes in A214828.

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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.

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A243622 Indices of primes in A214829.

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A243623 Prime terms in A214829.

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A244001 Indices of primes in A214830.

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A244002 Prime terms in A214830.

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A244930 Indices of primes in A214831.

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