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Category Archives: Math Beauty
Triangle (5, 7, 8)
A triangle with sides of length 5, 7, and 8 Perimeter = 20 Area = 10 √3 ~ 17.3205 one of its angles measures 60 degrees: Applying the Law … Continue reading
Using 1,2,3,4,5 only once to make 1 – 100
Game: Using 1, 2, 3, 4, 5 only once and the basic operations (+, -, * , / , !) to make all the numbers from 1 to 100 0 = 5 + 3 – (4*2/1) … Continue reading
Non-palindrome multiplied by its reverse is a square
For example, 288 is a non-palindrome and a non-square number. Its reverse is: Rev (288) = 882 and, 288 * 882 = 254016 = 504^2 is a perfect … Continue reading
DigitProduct and Sum of prime factors of numbers
(1) Integers such that the sum of prime factors equal the product of the digits of those integers: The prime factors of 18 are: … Continue reading
3-digit Num3ers w/ consecutive digits
123 + 132 + 213 + 231 + 312 + 321 = 1332 (123 + 132 + 213 + 231 + 312 + 321)/2 = 666 (123 + 132 + 213 + 231 + 312 + 321)/3 = 444 (123 … Continue reading
Num3ers such that (x+1)^3 – x^3 = y^2
OEIS – A001921 0, 7, 104, 1455, 20272, 282359, 3932760, 54776287, 762935264, 10626317415, 148005508552, 2061450802319, 28712305723920, 399910829332567, 5570039304932024, 77580639439715775, 1080558912851088832, 15050244140475527879, 209622859053806301480, … Continue reading
Concatenation | N||(N+1) and N||(N-1) are squares
N || (N + 1) = … Continue reading
Sum of 5 consecutive num3ers is a cube
Let (x-2), (x-1), x, (x+1), (x+2) be five consecutive integers. (x-2) + (x-1) + x + (x+1) + (x+2) = y^3 5*x = … Continue reading
Posted in Math Beauty, Number Puzzles
Tagged Consecutive Integers, Cubes, Squares, Sums
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Concatenation | Prime Num3ers
Smallest prime which is a concatenation of n distinct primes A083427 2 23 257 2357 112573 11132357 1113223537 111317193257 11131719223357 1113171922335437 111317192232934157 11131719223293135773 1113171922329313375759 111317192232931337415743 11131719223293133741435717 A088085 2 23 239 23911 23911313 23911313353 23911313353363 23911313353363373 239113133533633733993 23911313353363373399310401 2391131335336337339931040111911 … Continue reading
Num3er 504 – Puzzle
The factors of 504 are: 1 2 3 4 6 7 8 9 12 14 18 21 24 28 36 42 56 … Continue reading
