While I was chatting with one of my colleage over coffee, we discussed about 1729, Ramanujan number and how special the number was. I told my friend to look closely at the digits in pairs - 19 and 72, add both and you get 91 and now multiple 19 and 91 (which happen to be reverse of each other) - The answer is 1729!
Wow... There is something interesting about 91 he exclaimed and wanted to see if we can dig deeper.
The conversation started with the obvious - 91 is a product of two prime numbers 13 and 7. Well the next question was does 91 or its prime factors influence the number world in some way...
That discussion led to my next blog dedicated to 91! Here is a pattern that it influences right off the bat...
13 x 11 x 7 = 1001 (The first and last digit of the product is the number in the middle - 11)
13 x 12 x 7 = 1092 (first and last digit together is 12)
13 x 13 x 7 = 1183 (first and last digit together is 13)
13 x 14 x 7 = 1274 (first and last digit together is 14)
13 x 15 x 7 = 1365 (first and last digit together is 15)
13 x 16 x 7 = 1456 (first and last digit together is 16)
13 x 17 x 7 = 1547 (first and last digit together is 17)
13 x 18 x 7 = 1638 (first and last digit together is 18)
13 x 19 x 7 = 1729 (first and last digit together is 19 and ofcourse Ramanujan number!)
13 x 20 x 7 = 1820 (does not exhibit the same pattern but if you look closer 20 has sneaked in)
13 x 21 x 7 = 1911 (outlier again like the earlier one - Guess why?)
Now if you look at the first 9 output, look closely at the two digits in the middle - Yes you got it - They are multiples of 9 from 0 to 72 (9 * 0 till 9 * 8)
Now try to check the pattern from 22 onwards
13 x 22 x 7 = 2002 (the pattern has resumed!)
13 x 23 x 7 = 2093 (And it continues...)
Try to work on this sequence further and see where the pattern breaks again or rather where it becomes encapsulated as part of the output
Needless to say this behavioural pattern occurs due to a basic Mathematics principle and I am sure some of you have already figured that out!
Wow... There is something interesting about 91 he exclaimed and wanted to see if we can dig deeper.
The conversation started with the obvious - 91 is a product of two prime numbers 13 and 7. Well the next question was does 91 or its prime factors influence the number world in some way...
That discussion led to my next blog dedicated to 91! Here is a pattern that it influences right off the bat...
13 x 11 x 7 = 1001 (The first and last digit of the product is the number in the middle - 11)
13 x 12 x 7 = 1092 (first and last digit together is 12)
13 x 13 x 7 = 1183 (first and last digit together is 13)
13 x 14 x 7 = 1274 (first and last digit together is 14)
13 x 15 x 7 = 1365 (first and last digit together is 15)
13 x 16 x 7 = 1456 (first and last digit together is 16)
13 x 17 x 7 = 1547 (first and last digit together is 17)
13 x 18 x 7 = 1638 (first and last digit together is 18)
13 x 19 x 7 = 1729 (first and last digit together is 19 and ofcourse Ramanujan number!)
13 x 20 x 7 = 1820 (does not exhibit the same pattern but if you look closer 20 has sneaked in)
13 x 21 x 7 = 1911 (outlier again like the earlier one - Guess why?)
Now if you look at the first 9 output, look closely at the two digits in the middle - Yes you got it - They are multiples of 9 from 0 to 72 (9 * 0 till 9 * 8)
Now try to check the pattern from 22 onwards
13 x 22 x 7 = 2002 (the pattern has resumed!)
13 x 23 x 7 = 2093 (And it continues...)
Try to work on this sequence further and see where the pattern breaks again or rather where it becomes encapsulated as part of the output
Needless to say this behavioural pattern occurs due to a basic Mathematics principle and I am sure some of you have already figured that out!
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