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.

Previous Showing 31-38 of 38 results.

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

Views

Author

Robert Price, Feb 24 2015

Keywords

Comments

a(10) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A251747.

Programs

  • Mathematica
    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

Views

Author

Robert Price, Feb 24 2015

Keywords

Comments

a(9) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A251749.

Programs

  • Mathematica
    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

Views

Author

Robert Price, Feb 24 2015

Keywords

Comments

a(7) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A251750.

Programs

  • Mathematica
    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

Views

Author

Robert Price, Feb 24 2015

Keywords

Comments

a(5) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A251751.

Programs

  • Mathematica
    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

Views

Author

Robert Price, Feb 24 2015

Keywords

Comments

a(7) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A251752.

Programs

  • Mathematica
    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

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

Views

Author

Christoph B. Kassir, Jun 21 2021

Keywords

Comments

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)
...

Crossrefs

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

Programs

  • Maple
    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
  • Mathematica
    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 *)

Formula

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

A249169 Fibonacci 16-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-16).

Original entry on oeis.org

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65535, 131069, 262136, 524268, 1048528, 2097040, 4194048, 8388032, 16775936, 33551616, 67102720, 134204416, 268406784, 536809472, 1073610752, 2147205120, 4294377472, 8588689409
Offset: 15

Views

Author

Alan N. Inglis, Oct 22 2014

Keywords

Links

Crossrefs

Other k-step Fibonacci sequences: Cf. A000045, A000213, A000288, A000322, A000383, A060455, A123526, A127193, A127194, A168083, A207539, A168084, A220469, A220493.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<15, 0,
      `if`(n=15, 1, add(a(n-j), j=1..16)))
    end:
seq(a(n), n=15..50);  # Alois P. Heinz, Oct 23 2014
  • Mathematica
    CoefficientList[Series[-1 /(x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x - 1), {x, 0, 50}], x] (* Vincenzo Librandi, Nov 21 2014 *)

Formula

a(n) = a(n-1) + a(n-2) + ... + a(n-16).
G.f.: -x^15 / (x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5 +x^4+x^3+x^2+x-1). - Alois P. Heinz, Oct 23 2014

A345372 a(n) = Sum_{i=1..n} nac(i,n) where nac(i,n) is the n-th i-bonacci number. The n-th i-bonacci number here is equal to 1 for the first i terms, with subsequent terms equaling the sum of the previous n terms.

Original entry on oeis.org

1, 2, 4, 8, 16, 31, 60, 114, 217, 411, 780, 1481, 2820, 5379, 10288, 19720, 37884, 72924, 140640, 271695, 525698, 1018611, 1976276, 3838889, 7465191, 14531683, 28313776, 55214993, 107762464, 210477611, 411387724, 804609206, 1574671586, 3083549861, 6041628460
Offset: 1

Views

Author

Christoph B. Kassir, Jun 16 2021

Keywords

Comments

a(n) is the sum of the first n elements of the n-th column of the following array:
1, 1, 1, 1, 1, ... (1-bonacci numbers)
1, 1, 2, 3, 5, ... (2-bonacci or Fibonacci numbers)
1, 1, 1, 3, 5, ... (3-bonacci or tribonacci numbers)
1, 1, 1, 1, 4, ... (4-bonacci or tetranacci numbers)
...
For n >= 3, this sequence is 2 + antidiagonal sums of A061451.

Crossrefs

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

Programs

  • Maple
    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, n), i=1..n):
seq(a(n), n=1..36);  # Alois P. Heinz, Jun 16 2021
  • Mathematica
    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, n], {i, 1, n}];
Table[a[n], {n, 1, 36}] (* Jean-François Alcover, May 29 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{i=1..n} nac(i,n) where nac(i,n) = 1 if 1 <= n <= i, Sum_{k=1..i} nac(i,n-k) if n > i.
Previous Showing 31-38 of 38 results.

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