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 1-3 of 3 results.

A370664 Numbers k such that A176972(k) = 7^k + 7*k + 1 is prime.

Original entry on oeis.org

0, 5, 11, 1389, 5351, 6207, 31173
Offset: 1

Views

Author

Hugo Pfoertner, Feb 26 2024

Keywords

Comments

If it exists, a(8) > 50000.

Crossrefs

Programs

  • PARI
    is(n) = ispseudoprime(7^n+7*n+1)

A221909 a(n) = 7^n + 7*n.

Original entry on oeis.org

1, 14, 63, 364, 2429, 16842, 117691, 823592, 5764857, 40353670, 282475319, 1977326820, 13841287285, 96889010498, 678223072947, 4747561510048, 33232930569713, 232630513987326, 1628413597910575, 11398895185373276, 79792266297612141, 558545864083284154, 3909821048582988203
Offset: 0

Views

Author

Vincenzo Librandi, Mar 02 2013

Keywords

Crossrefs

Programs

  • Magma
    [7^n + 7*n: n in [0..30]];
    
  • Magma
    I:=[1, 14, 63]; [n le 3 select I[n] else 9*Self(n-1)-15*Self(n-2)+7*Self(n-3): n in [1..30]];
    
  • Mathematica
    Table[(7^n + 7 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 5 x - 48 x^2)/((1 - x)^2 (1 - 7 x)), {x, 0, 30}], x]
  • PARI
    a(n)=7^n+7*n \\ Charles R Greathouse IV, Apr 18 2013

Formula

G.f.: (1+5*x-48*x^2)/((1-x)^2*(1-7*x)).
a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3).
a(n) = A176972(n) - 1.
E.g.f.: exp(x)*(exp(6*x) + 7*x). - Elmo R. Oliveira, Sep 10 2024

A375577 Array read by ascending antidiagonals: A(n,k) = k^n + k*n + 1.

Original entry on oeis.org

2, 1, 2, 1, 3, 2, 1, 4, 5, 2, 1, 5, 9, 7, 2, 1, 6, 15, 16, 9, 2, 1, 7, 25, 37, 25, 11, 2, 1, 8, 43, 94, 77, 36, 13, 2, 1, 9, 77, 259, 273, 141, 49, 15, 2, 1, 10, 143, 748, 1045, 646, 235, 64, 17, 2, 1, 11, 273, 2209, 4121, 3151, 1321, 365, 81, 19, 2
Offset: 0

Views

Author

Stefano Spezia, Aug 19 2024

Keywords

Examples

			Array begins:
  2, 2,  2,   2,    2,     2, ...
  1, 3,  5,   7,    9,    11, ...
  1, 4,  9,  16,   25,    36, ...
  1, 5, 15,  37,   77,   141, ...
  1, 6, 25,  94,  273,   646, ...
  1, 7, 43, 259, 1045,  3151, ...
  1, 8, 77, 748, 4121, 15656, ...
  ...
		

Crossrefs

Cf. A000290, A004247, A004248, A005408 (n=1), A005491 (n=3), A007395 (n=0), A054977 (k=0), A176691 (k=2), A176805 (k=3), A176916 (k=5), A176972 (k=7), A214647.
Cf. A375578 (antidiagonal sums).

Programs

  • Mathematica
    A[0,0]=2; A[n_,k_]:=k^n+k*n+1;Table[A[n-k,k],{n,0,10},{k,0,n}]//Flatten

Formula

G.f. for the k-th column: (2*x^2 - 3*x - k^2 + k + 1)/((x - 1)^2*(x - k)).
E.g.f. for the k-th column: exp(x)*(1 + exp((k-1)*x) + k*x).
A(n,1) = n + 2.
A(2,n) = A000290(n+1).
A(n,n) = 2*A214647(n) + 1.
Showing 1-3 of 3 results.