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.

Showing 1-5 of 5 results.

A122498 Padovan numbers that are semiprimes.

Original entry on oeis.org

4, 9, 21, 49, 65, 86, 265, 1081, 1897, 2513, 7739, 97229, 128801, 299426, 922111, 1221537, 2839729, 62608681, 338356945, 53406819691, 2066337330754, 6363483400447, 8429820731201, 432062194544201, 7190854504969591, 12619069972000553, 16716708595637087
Offset: 1

Views

Author

Roger L. Bagula, Sep 15 2006

Keywords

Comments

The smallest candidate for the next term in the b-file is A000931(1958), which is composite with 239 digits and an unknown number of prime factors. - Hugo Pfoertner, Sep 07 2017

Crossrefs

Programs

  • Maple
    select(x-> numtheory[bigomega](x)=2, [(<<0|1|0>,
       <0|0|1>, <1|1|0>>^i)[1$2]$i=0..300])[];  # Alois P. Heinz, Aug 31 2017
  • Mathematica
    SemiprimeQ[1] := False SemiprimeQ[n_Integer] := Plus @@ (Last /@ FactorInteger[n]) == 2 a = Table[ SeriesCoefficient[ Series[x/(1 - x^2 - x^3), {x, 0, 50}], n], {n, 0, 50}] f[n_] = If[SemiprimeQ[a[[n]]] == True, a[[n]], {}] Flatten[Table[f[n], {n, 1, Length[a]}]]

Extensions

More terms from Alois P. Heinz, Aug 31 2017

A112882 Indices of prime Padovan numbers: values of k such that A000931(k+5) is prime.

Original entry on oeis.org

3, 4, 5, 7, 8, 14, 19, 30, 37, 84, 128, 469, 666, 1262, 1573, 2003, 2210, 2289, 4163, 5553, 6567, 8561, 11230, 18737, 35834, 44259, 536485, 727734
Offset: 1

Views

Author

Eric W. Weisstein, Oct 05 2005

Keywords

Crossrefs

Formula

a(n) = A152870(n) - 5. - Amiram Eldar, Nov 10 2024

Extensions

a(27) from Eric W. Weisstein, May 22 2009
a(28) from Eric W. Weisstein, Apr 10 2011

A291216 Padovan numbers that are also squares.

Original entry on oeis.org

0, 1, 4, 9, 16, 49
Offset: 1

Views

Author

Hugo Pfoertner, Aug 31 2017

Keywords

Comments

Common terms of A000931 and A000290.
Cited from Ian Stewart's article "Tales of a Neglected Number": "Some Padovan numbers, such as 9, 16 and 49, are perfect squares - are there others?"
No other terms < 10^(10^5). - Chai Wah Wu, Aug 31 2017

Crossrefs

A291673 Padovan numbers that are also Fibonacci numbers.

Original entry on oeis.org

0, 1, 2, 3, 5, 21
Offset: 1

Views

Author

Hugo Pfoertner, Aug 29 2017

Keywords

Comments

Common terms of A000931 and A000045.
Cited from Ian Stewart's article "Tales of a Neglected Number": "Some numbers, such as 3, 5 and 21, are both Fibonacci and Padovan. Are there others?"
In the b-files provided for both sequences, no further matches are found.
No other terms < 10^(10^5). - Chai Wah Wu, Aug 29 2017

Crossrefs

Programs

  • Mathematica
    With[{nn=100},Join[{0},Intersection[LinearRecurrence[{0,1,1},{1,1,2},nn],Fibonacci[Range[nn]]]]] (* Harvey P. Dale, Oct 09 2017 *)

A152870 Indices of primes in the Padovan sequence A000931.

Original entry on oeis.org

8, 9, 10, 12, 13, 19, 24, 35, 42, 89, 133, 474, 671, 1267, 1578, 2008, 2215, 2294, 4168, 5558, 6572, 8566, 11235, 18742, 35839, 44264, 536490, 727739
Offset: 1

Views

Author

Roger L. Bagula, Dec 14 2008

Keywords

Crossrefs

Programs

  • Mathematica
    a[0] = 1; a[1] = 0; a[2] = 0;
    a[n_] := a[n] = a[n - 2] + a[n - 3];
    Flatten[Table[If[PrimeQ[a[n]], n, {}], {n, 0, 10000}]]
  • PARI
    v=[1,1,1];for(n=8,1e4,v=[v[2],v[3],v[1]+v[2]];if(ispseudoprime(v[3]),print1(n", "))) \\ Charles R Greathouse IV, Nov 07 2011

Formula

a(n) = A112882(n) + 5. - Amiram Eldar, Nov 10 2024

Extensions

a(23)-a(26) from Charles R Greathouse IV, Nov 07 2011
a(27)-a(28) calculated from the data at A112882 by Amiram Eldar, Nov 10 2024
Showing 1-5 of 5 results.