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2. Triangular number - Wikipedia

   en.wikipedia.org/wiki/Triangular_number

   The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a ...

3. Centered triangular number - Wikipedia

   en.wikipedia.org/wiki/Centered_triangular_number

   Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number. Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular numbers. For n > 2, the sum of the first n centered triangular numbers is the magic constant for an n ...

4. Square triangular number - Wikipedia

   en.wikipedia.org/wiki/Square_triangular_number

   Consequently, a square number is also triangular if and only if + is square, that is, there are numbers and such that =. This is an instance of the Pell equation x 2 − n y 2 = 1 {\displaystyle x^{2}-ny^{2}=1} with n = 8 {\displaystyle n=8} .

5. Doubly triangular number - Wikipedia

   en.wikipedia.org/wiki/Doubly_triangular_number

   In mathematics, the doubly triangular numbers are the numbers that appear within the sequence of triangular numbers, in positions that are also triangular numbers. That is, if T n = n ( n + 1 ) / 2 {\displaystyle T_{n}=n(n+1)/2} denotes the n {\displaystyle n} th triangular number, then the doubly triangular numbers are the numbers of the form ...

6. 36 (number) - Wikipedia

   en.wikipedia.org/wiki/36_(number)

   The number of domino tilings of a 4×4 checkerboard is 36. [10] Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number. [11] The sum of the integers from 1 to 36 is 666 (see number of the beast). 36 is also a ...

7. List of numbers - Wikipedia, the free encyclopedia

   en.wikipedia.org/wiki/List_of_numbers

   A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.

8. Category:Triangles of numbers - Wikipedia

   en.wikipedia.org/wiki/Category:Triangles_of_numbers

   This page was last edited on 20 February 2023, at 19:48 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

9. Magic triangle (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Magic_triangle_(mathematics)

   In their magic triangles, the sum of the k-th row and the (n-k+1)-th row is same for all k. [5] (sequence A356808 in the OEIS) Its one modification uses triangular numbers instead of square numbers. (sequence A355119 in the OEIS) Another magic triangle form is magic triangles with triangular numbers with different summation. In this magic ...