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 1-2 of 2 results.

A274832 Values of n such that 2*n+1 and 7*n+1 are both triangular numbers (A000217).

Original entry on oeis.org

0, 27, 297, 24570, 267030, 22064157, 239792967, 19813588740, 215333817660, 17792580624687, 193369528466037, 15977717587380510, 173645621228683890, 14347972600887073617, 155933574493829667507, 12884463417879004727880, 140028176249837812737720
Offset: 1

Views

Author

Colin Barker, Jul 08 2016

Keywords

Comments

Intersection of A074377 and A274830.

Examples

			27 is in the sequence because 2*27+1 = 55, 7*27+1 = 190, and 55 and 190 are both triangular numbers.

Links

Crossrefs

Cf. A000217, A074377, A274830.
Cf. A124174 (2*n+1 and 9*n+1), A274579 (2*n+1 and 5*n+1), A274603 (2*n+1 and 3*n+1), A274680 (2*n+1 and 4*n+1), A274756 (2*n+1 and 7*n+1).

Programs

  • Mathematica
    LinearRecurrence[{1, 898, -898, -1, 1}, {0, 27, 297, 24570, 267030}, 20] (* Paolo Xausa, Oct 21 2024 *)
  • PARI
    isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(7*n+1, 3)
  • PARI
    concat(0, Vec(27*x^2*(1+10*x+x^2)/((1-x)*(1-30*x+x^2)*(1+30*x+x^2)) + O(x^20)))

Formula

G.f.: 27*x^2*(1+10*x+x^2) / ((1-x)*(1-30*x+x^2)*(1+30*x+x^2)).

A279042 Numbers k such that 2*k+1 and 10*k+1 are both triangular numbers (A000217).

Original entry on oeis.org

4455, 30537, 461938302, 3166172226, 47894687058501, 328275068740587, 4965816943137597372, 34036215673995404100, 514865832250497683700195, 3528942913182916419190605, 53382319214430283898266055610, 365887859090594924500524938502
Offset: 1

Views

Author

Colin Barker, Dec 04 2016

Keywords

Examples

			4455 is in the sequence because 2*4455+1 = 8911 and 10*4455+1 = 44551 are both triangular numbers.

Links

Crossrefs

Cf. A000217, A124174, A274579, A274603, A274680, A274756, A274832.

Programs

  • Mathematica
    LinearRecurrence[{1, 103682, -103682, -1, 1}, {4455, 30537, 461938302, 3166172226, 47894687058501}, 20] (* Vincenzo Librandi, Dec 05 2016 *)
  • PARI
    Vec(81*x*(55 + 322*x + 55*x^2) / ((1 - x)*(1 - 322*x + x^2)*(1 + 322*x + x^2)) + O(x^15))
  • PARI
    isok(k) = ispolygonal(2*k+1, 3) & ispolygonal(10*k+1, 3)

Formula

a(n) = a(n-1) + 103682*a(n-2) - 103682*a(n-3) - a(n-4) + a(n-5) for n>5.
G.f.: 81*x*(55 + 322*x + 55*x^2) / ((1 - x)*(1 - 322*x + x^2)*(1 + 322*x + x^2)).
Showing 1-2 of 2 results.

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

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