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 31-33 of 33 results.

A176593 List of pairs n,13*n.

Original entry on oeis.org

1, 13, 2, 26, 3, 39, 4, 52, 5, 65, 6, 78, 7, 91, 8, 104, 9, 117, 10, 130, 11, 143, 12, 156, 13, 169, 14, 182, 15, 195, 16, 208, 17, 221, 18, 234, 19, 247, 20, 260, 21, 273, 22, 286, 23, 299, 24, 312, 25, 325, 26, 338, 27, 351, 28, 364, 29, 377, 30, 390, 31, 403, 32, 416, 33
Offset: 1

Views

Author

Vincenzo Librandi, Apr 23 2010

Keywords

Links

Crossrefs

Cf. A008595.

Programs

  • Mathematica
    Table[{n,13n},{n,50}]//Flatten (* or *) LinearRecurrence[{0,2,0,-1},{1,13,2,26},100] (* Harvey P. Dale, Oct 16 2019 *)
  • PARI
    Vec(x*(1+13*x) / ((1-x)^2*(1+x)^2) + O(x^30)) \\ Colin Barker, Jan 02 2017

Formula

a(n) = (14*n+12*n*(-1)^n+1 + (-1)^(n-1))/4 for n>1.
From Colin Barker, Jan 02 2017: (Start)
a(n) = 2*a(n-2) - a(n-4) for n>4.
G.f.: x*(1+13*x) / ((1-x)^2*(1+x)^2).
(End)

Extensions

Partially edited by N. J. A. Sloane, Jun 23 2010

A230215 Numbers divisible by 3 or 13.

Original entry on oeis.org

3, 6, 9, 12, 13, 15, 18, 21, 24, 26, 27, 30, 33, 36, 39, 42, 45, 48, 51, 52, 54, 57, 60, 63, 65, 66, 69, 72, 75, 78, 81, 84, 87, 90, 91, 93, 96, 99, 102, 104, 105, 108, 111, 114, 117, 120, 123, 126, 129, 130, 132, 135, 138, 141, 143, 144, 147, 150, 153, 156
Offset: 1

Views

Author

Gary Detlefs, Oct 11 2013

Keywords

Comments

In general, sequences of numbers divisible by primes p and q will have the form a(n+p+q-1) = a(n) + p*q.
Union of A008585 and A008595 (0 excluded). - Michel Marcus, Oct 16 2013
The asymptotic density of this sequence is 5/13. - Amiram Eldar, Mar 25 2021

Links

Crossrefs

Complement of A229973.
Cf. A008585, A008595.

Programs

  • Maple
    for n from 1 to 138 do if n mod 3 = 0 or n mod 13= 0 then print(n) fi od
  • Mathematica
    Select[Range[200], GCD[#, 39] > 1 &] (* T. D. Noe, Oct 15 2013 *)
With[{nn=60},Join[3*Range[nn],13*Floor[3/13 Range[nn]]]]//Union//Rest (* Harvey P. Dale, May 25 2020 *)
  • PARI
    is(n)=gcd(n,39)>1 \\ Charles R Greathouse IV, Dec 11 2013

Formula

a(n+15) = a(n) + 39.

A324270 a(n) = 13*7^(7*n).

Original entry on oeis.org

13, 10706059, 8816899947037, 7261096233082692091, 5979824975081619492698413, 4924642999453642161875329137259, 4055655269699050826917294183685688637, 3340006507773765415151949203915063077180891, 2750638979431530091290481703239822791770782516813, 2265269477037980585971637173331233381403285546243728459
Offset: 0

Views

Author

Stefano Spezia, Mar 22 2019

Keywords

Comments

x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(14*n+3) = 4*y^7 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).

Examples

			For a(0) = 13 and A324266(0) = 2, 13^2 + 7^3 = 512 = 4*2^7.

Links

Crossrefs

Cf. A324266 (2*49^n), A001015 (seventh powers), A000420 (powers of 7), A008595 (multiples of 13).

Programs

  • GAP
    List([0..20], n->13*823543^n);
  • Magma
    [13*823543^n: n in [0..20]];
  • Maple
    a:=n->13*823543^n: seq(a(n), n=0..20);
  • Mathematica
    13 823543^Range[0, 20]
  • PARI
    a(n) = 13*823543^n;

Formula

O.g.f.: 13/(1 - 823543*x).
E.g.f.: 13*exp(823543*x).
a(n) = 823543*a(n-1) for n > 0.
a(n) = 13*823543^n.
a(n) = A008595(A001015((A000420(n)))).
Previous Showing 31-33 of 33 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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