James Magan
New member
- Joined
- Nov 27, 2013
- Messages
- 17
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M
1.
I believe that the numbers 153, 370, 371 and 407 are the only four "known" numbers which have this property: if you sum the cube of the digits in each number, you get the original number (so in the case of 153, for example, 1 + 125 + 27 = 153).
Can anyone tell me, please, how far mathematical "knowledge" is likely to stretch in this regard: into the thousands? tens of thousands? millions? beyond? Or in other words, what is the "cieling" below which we can say with certainty that there is no other number that has the same property as the four numbers already mentioned?
2.
153 is a triangular number. I would like to access online, or generate on rapidly on an Excel spreadsheet if that is possible, a list of all triangular numbers up to about 1,000,000. I guess that may not be too difficult for a mathematician: could somebody tell me how to do it, please.
3.
3 is a triangular number: it completes the second line of the triangle if you count 1 as being the first line. 3 is also the sum of 1! + 2!.
153 is a triangular number: it completes line 17 of the triangle. 153 is also the sum of 1! + 2! + 3! + 4! + 5!
I would like to be able to view or generate a list of the sums of 1! + 2!; ... 1! + 2! + 3! ; ... 1! + 2! + 3! + 4!; ... 1! + 2! + 3! + 4! + 5!, and so on , increasing by one digit at a time, until the product again reaches about 1,000,000. Could someone tell me how to do that, please.
(I want to know if any other numbers apart from 3 and 153 share the two properties mentioned above.)
Many thanks
M
1.
I believe that the numbers 153, 370, 371 and 407 are the only four "known" numbers which have this property: if you sum the cube of the digits in each number, you get the original number (so in the case of 153, for example, 1 + 125 + 27 = 153).
Can anyone tell me, please, how far mathematical "knowledge" is likely to stretch in this regard: into the thousands? tens of thousands? millions? beyond? Or in other words, what is the "cieling" below which we can say with certainty that there is no other number that has the same property as the four numbers already mentioned?
2.
153 is a triangular number. I would like to access online, or generate on rapidly on an Excel spreadsheet if that is possible, a list of all triangular numbers up to about 1,000,000. I guess that may not be too difficult for a mathematician: could somebody tell me how to do it, please.
3.
3 is a triangular number: it completes the second line of the triangle if you count 1 as being the first line. 3 is also the sum of 1! + 2!.
153 is a triangular number: it completes line 17 of the triangle. 153 is also the sum of 1! + 2! + 3! + 4! + 5!
I would like to be able to view or generate a list of the sums of 1! + 2!; ... 1! + 2! + 3! ; ... 1! + 2! + 3! + 4!; ... 1! + 2! + 3! + 4! + 5!, and so on , increasing by one digit at a time, until the product again reaches about 1,000,000. Could someone tell me how to do that, please.
(I want to know if any other numbers apart from 3 and 153 share the two properties mentioned above.)
Many thanks