A214825 -id:A214825 - cp's OEIS frontend

A230016 Indices of primes in the tribonacci-like sequence, A214825.

1, 2, 3, 4, 5, 6, 7, 10, 16, 17, 26, 32, 104, 109, 120, 133, 312, 546, 608, 2274, 2527, 2932, 4462, 4680, 6001, 7103, 17402, 17874, 20664, 26341, 27954, 32869, 36204, 41521, 49065, 64172, 66318, 196078

Offset: 1

Robert Price, Feb 22 2014

nonn

a(39) > 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.

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

A230017 Prime terms in the tribonacci-like sequence, A214825.

Original entry on oeis.org

3, 3, 7, 13, 23, 43, 79, 491, 19009, 34963, 8422747, 326099713, 3699221592878859104602113553, 77867739062209443974741001359, 63460200981504216633346603450897, 174962190954783387911511685367053207

Offset: 1

Robert Price, Feb 22 2014

nonn

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

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

A214727 a(n) = a(n-1) + a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 2.

Original entry on oeis.org

1, 2, 2, 5, 9, 16, 30, 55, 101, 186, 342, 629, 1157, 2128, 3914, 7199, 13241, 24354, 44794, 82389, 151537, 278720, 512646, 942903, 1734269, 3189818, 5866990, 10791077, 19847885, 36505952, 67144914, 123498751, 227149617, 417793282

Offset: 0

Abel Amene, Jul 27 2012

Part of a group of sequences defined by a(0), a(1)=a(2), a(n) = a(n-1) + a(n-2) + a(n-3) which is a subgroup of sequences with linear recurrences and constant coefficients listed in the index.
Note: A000073 (with offset=1), 1 followed by A000073, A000213, A141523, A214727, A214825 to A214831 completely define possible sequences with a(0)=0,1,2...9 and a(1)=a(2)=0,1,2...9 excluding any multiples of these sequences and the trivial case of a(0)=a(1)=a(2)=0.
Note: allowing a(0)=0 and a(1)=a(2)=1,2,3....9 leads to A000073 (with offset=1) and its multiples.
Note: allowing a(0)=1,2,3....9 a(1)=a(2)=0 leads to 1 followed by A000073 and its multiples.
With offset of 6 this sequence is the 8th row of tribonacci array A136175.

			G.f. = 1 + 2*x + 2*x^2 + 5 x^3 + 9*x^4 + 16*x^5 + 30*x^6 + 55*x^7 + ...

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Martin Burtscher, Igor Szczyrba, and Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
Index entries for linear recurrences with constant coefficients, signature (1,1,1).

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

a:=[1,2,2];; 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

a214727 n = a214727_list !! n
a214727_list = 1 : 2 : 2 : zipWith3 (\x y z -> x + y + z)
   a214727_list (tail a214727_list) (drop 2 a214727_list)
-- Reinhard Zumkeller, Jul 31 2012

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 23 2019

LinearRecurrence[{1,1,1},{1,2,2},40] (* Ray Chandler, Dec 08 2013 *)

a(n)=([0,1,0; 0,0,1; 1,1,1]^n*[1;2;2])[1,1] \\ Charles R Greathouse IV, Mar 22 2016

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

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

G.f.: (1+x-x^2)/(1-x-x^2-x^3).
a(n) = K(n) -2*T(n+1) + 3*T(n), where K(n) = A001644(n), T(n) = A000073(n+1). - G. C. Greubel, Apr 23 2019
a(n) = Sum_{r root of x^3-x^2-x-1} r^n/(-r^2+2*r+1). - Fabian Pereyra, Nov 20 2024

A214827 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 5.

Original entry on oeis.org

1, 5, 5, 11, 21, 37, 69, 127, 233, 429, 789, 1451, 2669, 4909, 9029, 16607, 30545, 56181, 103333, 190059, 349573, 642965, 1182597, 2175135, 4000697, 7358429, 13534261, 24893387, 45786077, 84213725, 154893189, 284892991, 523999905

Offset: 0

Abel Amene, Jul 29 2012

See comments in A214727.

Robert Price, Table of n, a(n) for n = 0..1000
Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
Index entries for linear recurrences with constant coefficients, signature (1,1,1).

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

a:=[1,5,5];; 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+4*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019

LinearRecurrence[{1,1,1},{1,5,5},40] (* Ray Chandler, Dec 08 2013 *)

my(x='x+O('x^40)); Vec((1+4*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 24 2019

((1+4*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019

G.f.: (x^2-4*x-1)/(x^3+x^2+x-1).

a(n) = -A000073(n) + 4*A000073(n+1) + A000073(n+2). - R. J. Mathar, Jul 29 2012

A214831 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 9.

Original entry on oeis.org

1, 9, 9, 19, 37, 65, 121, 223, 409, 753, 1385, 2547, 4685, 8617, 15849, 29151, 53617, 98617, 181385, 333619, 613621, 1128625, 2075865, 3818111, 7022601, 12916577, 23757289, 43696467, 80370333, 147824089, 271890889, 500085311, 919800289, 1691776489

Offset: 0

Abel Amene, Aug 07 2012

Part of a group of sequences defined by a(0), a(1)=a(2), a(n)=a(n-1)+a(n-2)+a(n-3) which is a subgroup of sequences with linear recurrences and constant coefficients listed in the index. 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-A214831, A244930, A244931.

a:=[1,9,9];; 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+8*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019

LinearRecurrence[{1,1,1},{1,9,9},40] (* Harvey P. Dale, Oct 11 2017 *)

Vec((x^2-8*x-1)/(x^3+x^2+x-1) + O(x^40)) \\ Michel Marcus, Jul 08 2014

((1+8*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+8*x-x^2)/(1-x-x^2-x^3).

a(n) = -A000073(n) + 8*A000073(n+1) + A000073(n+2). - G. C. Greubel, Apr 24 2019

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

Robert Price, Dec 03 2014

nonn

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

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.

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]

A214828 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 6.

Original entry on oeis.org

1, 6, 6, 13, 25, 44, 82, 151, 277, 510, 938, 1725, 3173, 5836, 10734, 19743, 36313, 66790, 122846, 225949, 415585, 764380, 1405914, 2585879, 4756173, 8747966, 16090018, 29594157, 54432141, 100116316, 184142614, 338691071, 622950001

Offset: 0

Abel Amene, Jul 30 2012

See comments in A214727.

Robert Price, Table of n, a(n) for n = 0..1000
Martin Burtscher, Igor Szczyrba, and Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
Index entries for linear recurrences with constant coefficients, signature (1,1,1).

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

a:=[1,6,6];; 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+5*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019

LinearRecurrence[{1,1,1},{1,6,6},33] (* Ray Chandler, Dec 08 2013 *)

my(x='x+O('x^40)); Vec((1+5*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 24 2019

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

a(n) = -A000073(n) + 5*A000073(n+1) + A000073(n+2). - G. C. Greubel, Apr 24 2019

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

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

Robert Price, Sep 09 2014

a(14) > 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, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523,A214825, A235862.

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

Robert Price, Apr 26 2014

nonn

a(15) > 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.

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]

Prepended a(1)=3 and Mathematica program corrected by Robert Price, Sep 09 2014

cp's OEIS Frontend

A230016 Indices of primes in the tribonacci-like sequence, A214825.

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A230017 Prime terms in the tribonacci-like sequence, A214825.

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A214727 a(n) = a(n-1) + a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 2.

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A214827 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 5.

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A214831 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 9.

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A249413 Primes in the hexanacci numbers sequence A000383.

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A214828 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 6.

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