1. It is the 8th abundant number
2. It lies between twin prime numbers 41 and 43.
3. It is the smallest perfect square that is the mean of two cubed primes.
422 = (113 + 133 ) / 2
4. It is the sum of first 6 even numbers.
42 = 2 + 4 + 6 + 8 + 10 + 12
5. n^2 – n is divisible by 42.
6. The 3 x 3 x 3 magic cube can be constructed with the help of numbers from 1to 27 such that the sum of every row, column and diagonal is 42.
7. It can be partitioned into 44583 ways.
8. It is a repdigit in base 4.
42 = (222)4
9. The atomic number of molybdenum is 42.
10. It is the product of first three terms of Sylvester’s sequence. Sylvester’s sequence is named after the mathematician James Joseph Sylvester. Sylvester’s sequence is an integer sequence in which each member of the sequence is the product of the previous members plus one. The first five members of Sylvester’s sequence is --- 2, 3, 7, 43 and 1807.
42 = 2 x 3 x 7
11. It is the reciprocal of sixth Bernoulli numbers (1/42) discovered by great Swiss mathematician Jakob Bernoulli. The first few Bernoulli numbers are--
B0 = 1, B1 = ±1⁄2, B2 = 1⁄6, B3 = 0, B4 = −1⁄30, B5 = 0, B6 = 1⁄42, B7 = 0, B8 = −1⁄30.
12. It is a Catalan number. The series for Catalan numbers are--- 1, 1, 2, 5, 14, 42, 132, 429---.Catalan numbers are probably the most frequently occurring combinatorial numbers, after the binomial coefficients. It is named after the Belgian mathematician Eugene Charles Catalan. The nth Catalan number is defined as --
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
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