World!OfNumbers |
WON plate 89 | |
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[ June 20, 1999 I received a message from 11th grader Kiwoo Songasking for extra material related to a particular theorem... Honesty compells me to say I couldn't help him further with the project but found the theorem nevertheless very intriguing as it relates two familar concepts in a very interesting way namely factorials and binary numbers. Any natural number N is equal to the sum of the numbers of 1's in its A few worked out examples to illustrate the topic Take N = 9 Take N = 79 Just like Kiwoo Song then I am now trying to find information It was Legendre that first found the results in 1808. Sum N/q^i from i=0 to inf = [N/q] + [N/q^2] + [N/q^3] + ... + [N/q^n] + 0 + 0 + ... where [x] = greatest integer less than or equal to x. He also said that the difference between the number N and the sum
The number of 1s in the binary expression of N is also known as The proof is not too difficult to find. Can it be found on the web ? | ||||

A000089 Prime Curios! Prime Puzzle Wikipedia 89 Le Nombre 89 Numberland 89 |

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