The well known Armstrong numbers are 153, 370, 371, 407 (apart from 0 and 1). Here are few more patterns exhibited by these numbers around squares, cubes and prime numbers
While most of the natural numbers will exhibit pattern of these sorts, it is interesting to see how fe number pairs play a larger role for these 4 numbers
a) 153
12 ^ 2 + 3 ^ 2
13 ^ 2 - 4 ^ 2
One of the anagram of 153 is 513 is 8 ^ 3 + 1 ^ 3
b) 370
7 ^ 3 + 3 ^ 3
19 ^ 2+ 3 ^ 2
One of the anagrams of 370 is 703 (which is not an Armstrong number but check the pattern)
703 = 19 x 37 (19 is there in earlier pattern exhibited by 370 and 37 is a subset of 370!)
c) 371
7 ^ 3 + 3 ^ 3 + 1 ^ 3 (sub of 3 different cubes)
One of the anagram of 371 is 731 which is formed by the digits 7, 3, 1 again
d) 407
7 ^ 3 + 4 ^ 3 or 7 ^ 3 + 8 ^ 2
Its anagram 704 is 7 ^ 3 + 19 ^ 2 (again notice the role number 19 plays in some of these numbers)
Last but not the least the Armstrong numbers show intricate relationship pattern among themselves
407 in turn is 370 + 37 (effectively 37 * 10, 37 * 11)
407 is also 371 + 6 ^ 2
While most of the natural numbers will exhibit pattern of these sorts, it is interesting to see how fe number pairs play a larger role for these 4 numbers
a) 153
12 ^ 2 + 3 ^ 2
13 ^ 2 - 4 ^ 2
One of the anagram of 153 is 513 is 8 ^ 3 + 1 ^ 3
b) 370
7 ^ 3 + 3 ^ 3
19 ^ 2+ 3 ^ 2
One of the anagrams of 370 is 703 (which is not an Armstrong number but check the pattern)
703 = 19 x 37 (19 is there in earlier pattern exhibited by 370 and 37 is a subset of 370!)
c) 371
7 ^ 3 + 3 ^ 3 + 1 ^ 3 (sub of 3 different cubes)
One of the anagram of 371 is 731 which is formed by the digits 7, 3, 1 again
d) 407
7 ^ 3 + 4 ^ 3 or 7 ^ 3 + 8 ^ 2
Its anagram 704 is 7 ^ 3 + 19 ^ 2 (again notice the role number 19 plays in some of these numbers)
Last but not the least the Armstrong numbers show intricate relationship pattern among themselves
407 in turn is 370 + 37 (effectively 37 * 10, 37 * 11)
407 is also 371 + 6 ^ 2
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