This site is supported by donations to The OEIS Foundation.

Template:Sequence of the Day for December 1

From OeisWiki

Jump to: navigation, search

Intended for: December 1, 2011

Timetable

  • First draft entered by Alonso del Arte on August 28, 2011 ✓
  • Draft reviewed by Daniel Forgues on December 1, 2011 ✓
  • Draft to be approved by November 1, 2011
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.


A188892: Numbers \scriptstyle n \, such that there is no triangular \scriptstyle n \,-gonal number greater than 1.

{ 11, 18, 38, 102, 198, 326, 486, ... }

The triangular numbers are essentially the building blocks of the other figurate numbers. Therefore it is rather surprising that there can be sequences of \scriptstyle n \,-gonal numbers that don't overlap with the sequence of triangular numbers at all (other than 0 and 1.) T. D. Noe has demonstrated that the equation \scriptstyle x^2 + x \,=\, (n - 2)y^2 - (n - 4)y \, has no integer solutions \scriptstyle x \,\geq\, y \,>\, 1 \,, as conversion to a generalized Pell equation shows that if \scriptstyle n \,=\, k^2 + 2 \,, then the first equation has only a finite number of solutions. From there one can pinpoint those values of \scriptstyle n \, that produce no integer solutions greater than 1.

Retrieved from "http://oeis.org/wiki/Template:Sequence_of_the_Day_for_December_1"
Personal tools