A000322 -id:A000322 - cp's OEIS frontend

A255529 Indices of primes in the 9th-order Fibonacci number sequence, A104144.

10, 19, 878

Offset: 1

Robert Price, Feb 24 2015

a(4) > 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, A000288, A000322, A000383, A249413, A060455, A079262, A104144.

a={0,0,0,0,0,0,0,0,1}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

a104144(n) = polcoeff(x^8/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9) + O(x^(n+1)), n);
lista(nn) = {for (n=1, nn, if (isprime(a104144(n)), print1(n, ", ")););} \\ Michel Marcus, Feb 27 2015

A255530 Indices of primes in the 9th-order Fibonacci number sequence, A251746.

Original entry on oeis.org

10, 19, 59, 79, 12487

Offset: 1

Robert Price, Feb 24 2015

a(6) > 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, A000288, A000322, A000383, A249413, A060455, A079262, A251746.

a={0,0,0,0,0,0,0,1,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

A255531 Indices of primes in the 9th-order Fibonacci number sequence, A251747.

Original entry on oeis.org

10, 16, 116, 236, 316, 1376, 5066, 103696, 120949

Offset: 1

Robert Price, Feb 24 2015

a(10) > 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, A000288, A000322, A000383, A249413, A060455, A079262, A251747.

a={0,0,0,0,0,0,1,0,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst
Flatten[Position[LinearRecurrence[Table[1,{9}],{0,0,0,0,0,0,1,0,0},125000],?PrimeQ]]-1 (* _Harvey P. Dale, Nov 29 2017 *)

A255532 Indices of primes in the 9th-order Fibonacci number sequence, A251749.

Original entry on oeis.org

10, 14, 19, 29, 404, 1744, 8854, 27754

Offset: 1

Robert Price, Feb 24 2015

a(9) > 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, A000288, A000322, A000383, A249413, A060455, A079262, A251749.

a={0,0,0,0,1,0,0,0,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

A255533 Indices of primes in the 9th-order Fibonacci number sequence, A251750.

Original entry on oeis.org

10, 33, 43, 253, 1253, 2389

Offset: 1

Robert Price, Feb 24 2015

a(7) > 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, A000288, A000322, A000383, A249413, A060455, A079262, A251750.

a={0,0,0,1,0,0,0,0,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

A255534 Indices of primes in the 9th-order Fibonacci number sequence, A251751.

Original entry on oeis.org

10, 12, 232, 502

Offset: 1

Robert Price, Feb 24 2015

a(5) > 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, A000288, A000322, A000383, A249413, A060455, A079262, A251751.

a={0,0,1,0,0,0,0,0,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst
Flatten[Position[LinearRecurrence[Table[1,{9}],{0,0,1,0,0,0,0,0,0},510], ?(PrimeQ[#]&)]]-1 (* _Harvey P. Dale, Feb 27 2016 *)

A255536 Indices of primes in the 9th-order Fibonacci number sequence, A251752.

Original entry on oeis.org

10, 11, 21, 29, 301, 57089

Offset: 1

Robert Price, Feb 24 2015

a(7) > 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, A000288, A000322, A000383, A249413, A060455, A079262, A251752.

a={0,1,0,0,0,0,0,0,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

A259615 a(0)=0, a(1)=a(2)=a(3)=a(4)=1; thereafter, a(n) = Sum_{k=1..5} a(n-k-(a(n-k) mod 5)).

Original entry on oeis.org

0, 1, 1, 1, 1, 3, 4, 5, 9, 9, 11, 19, 23, 27, 45, 87, 105, 205, 401, 587, 747, 1121, 1763, 2145, 4085, 7965, 15529, 16545, 32503, 38323, 49767, 74305, 146847, 180069, 210427, 341745, 650987, 787109, 917411

Offset: 0

Anders Hellström, Jun 30 2015

nonn

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

Cf. A000322, A241154 (sequence obtained without mod 5 in formula).

def first(m)
    v=[0,1,1,1,1]
    for i in 5..m-1
      i2=0
      for j in 1..5
        r=i-j
        i2 += v[r-v[r]%5]
      end
      v << i2
    end
    v
end

def first(m):
    v=[0,1,1,1,1]
    for i in range(5,m+1):
      l=0
      for s in range(1,5+1):
        l += v[i-s-v[i-s]%5]
      v.append(l)
    return v

A345669 Antidiagonal sums of array containing i-bonacci sequences nac(i,n), where nac(i,n) is the n-th i-bonacci number with nac(i,1..i) = 1 (see comments).

Original entry on oeis.org

1, 2, 3, 5, 7, 12, 18, 31, 51, 89, 153, 273, 483, 870, 1571, 2860, 5225, 9603, 17711, 32805, 60967, 113685, 212610, 398723, 749615, 1412585, 2667549, 5047345, 9567527, 18166272, 34546857, 65793343, 125471295, 239584610, 458028439, 876628109, 1679581899

Offset: 1

Christoph B. Kassir, Jun 21 2021

nonn

Antidiagonal sum of below array:
1, 1, 1, 1, 1, 1, ... (1-bonacci numbers)
1, 1, 2, 3, 5, 8, ... (2-bonacci or Fibonacci numbers)
1, 1, 1, 3, 5, 9, ... (3-bonacci or tribonacci numbers)
1, 1, 1, 1, 4, 7, ... (4-bonacci or tetranacci numbers)
...

Cf. A000045, A000213, A000288, A000322, A000383, A060455, A061451.

b:= proc(i, n) option remember; `if`(n=0, 0,
      `if`(n<=i, 1, add(b(i, n-j), j=1..i)))
    end:
a:= n-> add(b(i+1, n-i), i=0..n):
seq(a(n), n=1..37);  # Alois P. Heinz, Jun 21 2021

b[i_, n_] := b[i, n] = If[n == 0, 0, If[n <= i, 1, Sum[b[i, n - j], {j, 1, i}]]];
a[n_] := Sum[b[i + 1, n - i], {i, 0, n}];
Table[a[n], {n, 1, 37}] (* Jean-François Alcover, Dec 27 2022, after Alois P. Heinz *)

a(n) = Sum_{i=1..n} of nac(i,n-i+1) = Sum_{i=1..n} of nac(n-i+1,i).

A112678 Sum of digits of previous 5 terms.

Original entry on oeis.org

1, 1, 1, 1, 1, 5, 9, 8, 6, 11, 12, 10, 11, 5, 13, 6, 9, 8, 5, 5, 6, 6, 3, 7, 9, 4, 11, 7, 11, 6, 12, 11, 11, 6, 10, 5, 7, 12, 4, 11, 12, 10, 13, 5, 6, 10, 8, 6, 8, 11, 7, 4, 9, 12, 7, 12, 8, 12, 6, 9, 11, 10, 12, 12, 9, 9, 7, 13, 5, 7, 5, 10, 4, 4, 3, 8, 11, 3, 11, 9, 6, 4, 6, 9, 7, 5, 4, 4, 11, 4

Offset: 0

Jonathan Vos Post, Dec 30 2005

This is to the pentanacci sequence A001591 as A112661 is to the tribonacci and as A030132 is to Fibonacci. A000322 is the pentanacci sequence (A001591) but starting with values (1,1,1,1,1). Andrew Carmichael Post (andrewpost(AT)gmail.com) wrote the program that generated this sequence and showed that for any 5 initial integers a(0),a(1),a(2),a(3),a(4) the length of the cycle eventually entered is a factor of 2184. For the SOD(teranacci) the limit cycle length is always a factor of 312. For the SOD(tribonacci) which is A112661, the length of any cycle eventually entered is a factor of 78.

			a(0)=a(1)=a(2)=a(3)=a(4)=1.
a(5) = SOD(1+1+1+1+1) = SOD(5) = 5.
a(6) = SOD(1+1+1+1+5) = SOD(9) = 9.
a(7) = SOD(1+1+1+5+9) = SOD(17) = 8.
a(8) = SOD(1+1+5+9+8) = SOD(24) = 6.
a(9) = SOD(1+5+9+8+6) = SOD(29) = 11, note that we do not iterate SOD to reduce 11 to 2.

Cf. A000322, A001591, A004090, A007953, A010888, A030132, A112661.

a(0)=a(1)=a(2)=a(3)=a(4)=1. a(n) = SumDigits(a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)). a(n) = SumDigits(A000322(n)).

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A255529 Indices of primes in the 9th-order Fibonacci number sequence, A104144.

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A255530 Indices of primes in the 9th-order Fibonacci number sequence, A251746.

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A255531 Indices of primes in the 9th-order Fibonacci number sequence, A251747.

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A255532 Indices of primes in the 9th-order Fibonacci number sequence, A251749.

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A255533 Indices of primes in the 9th-order Fibonacci number sequence, A251750.

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A255534 Indices of primes in the 9th-order Fibonacci number sequence, A251751.

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A255536 Indices of primes in the 9th-order Fibonacci number sequence, A251752.

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A259615 a(0)=0, a(1)=a(2)=a(3)=a(4)=1; thereafter, a(n) = Sum_{k=1..5} a(n-k-(a(n-k) mod 5)).

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A345669 Antidiagonal sums of array containing i-bonacci sequences nac(i,n), where nac(i,n) is the n-th i-bonacci number with nac(i,1..i) = 1 (see comments).

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