Forty-nine is the square of the prime number
seven and hence the fourth non-unitary square
prime of the form
p2. Both of its digits are square numbers, 4 being the square of 2 and 9 being the square of 3. It appears in the
Padovan sequence, preceded by the terms 21, 28, 37 (it is the sum of the first two of these). Along with the number that immediately derives from it, 77, the only number under
100 not having its
home prime known (). The smallest triple of three squares in arithmetic succession is (1,25,49), and the second smallest is (49,169,289). 49 is the smallest
discriminant of a
totally real cubic field. 49 and 94 are the only numbers below 100 whose all permutations are composites but they are not multiples of 3, repdigits or numbers which only have digits 0, 2, 4, 5, 6 and 8, even excluding the trivial one digit terms. 49 = 7^2 and 94 = 2 * 47 The number of
prime knots with 9 crossings is 49.
Decimal representation The sum of the digits of the square of 49 (2401) is the square root of 49. 49 is the first square where the digits are squares. In this case, 4 and 9 are squares.
Reciprocal The fraction is a repeating decimal with a period of 42: : = (42 digits repeat) There are 42 positive integers less than 49 and coprime to 49. (42 is the period.) Multiplying 020408163265306122448979591836734693877551 by each of these integers results in a
cyclic permutation of the original number: • 020408163265306122448979591836734693877551 × 2 = 040816326530612244897959183673469387755102 • 020408163265306122448979591836734693877551 × 3 = 061224489795918367346938775510204081632653 • 020408163265306122448979591836734693877551 × 4 = 081632653061224489795918367346938775510204 • ... The repeating number can be obtained from 02 and repetition of doubles placed at two places to the right: 02 04 08 16 32 64 128 256 512 1024 2048 + ... ---------------------- 020408163265306122448979591836734693877551...0204081632... because satisfies: :x = \frac{1}{50} + \frac{2x}{100} = \frac{1}{50}(1 + x)\, . ==In chemistry==