Search results
Results From The WOW.Com Content Network
For example, the third triangular number is (3 × 2 =) 6, the seventh is (7 × 4 =) 28, the 31st is (31 × 16 =) 496, and the 127th is (127 × 64 =) 8128. 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.
the number of vertices in a 6-cube, the fourth dodecagonal number, [8] and the seventh centered triangular number. [9] Since it is possible to find sequences of 65 consecutive integers (intervals of length 64) such that each inner member shares a factor with either the first or the last member, 64 is the seventh Erdős–Woods number. [10]
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
For example, each centered square number in the series is four times the previous triangular number, plus 1. This can be formalized by the expression (+) +. These series consist of the centered triangular numbers 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166
The triangular number sequence is the representation of the numbers in the form of equilateral triangle arranged in a series or sequence. These numbers are in a sequence of 1, 3, 6, 10, 15, 21, 28, 36, 45, and so on.
The difference of two positive triangular numbers is a trapezoidal number. Gnomon The gnomon is the ... the figure illustrates 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 ...
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 ...
Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9. The digital root pattern, repeating every nine terms, is "1 6 6 1 9 3 1 3 9". Every even perfect number is hexagonal, given by the formula = + = (+) / = where M p is a Mersenne prime. No odd perfect numbers are known, hence all known perfect ...