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Problem 700


Problem 700


Eulercoin

Leonhard Euler was born on 15 April 1707.

Consider the sequence 1504170715041707nmod4503599627370517.

An element of this sequence is defined to be an Eulercoin if it is strictly smaller than all previously found Eulercoins.

For example, the first term is 1504170715041707 which is the first Eulercoin. The second term is 3008341430083414 which is greater than 1504170715041707 so is not an Eulercoin. However, the third term is 8912517754604 which is small enough to be a new Eulercoin.

The sum of the first 2 Eulercoins is therefore 1513083232796311.

Find the sum of all Eulercoins.


欧拉币

莱昂哈德·欧拉出生于1707年四月15日。

考虑序列1504170715041707nmod4503599627370517

该序列中的某个元素被定义为欧拉币,当且仅当它严格小于之前已经定义的所有欧拉币。

例如,序列的第一项是1504170715041707,这是第一枚欧拉币。序列的第二项是3008341430083414,因为它大于1504170715041707,因此它不是欧拉币。然后,序列的第三项是8912517754604,比第一项要小,因此是一枚新的欧拉币。

因此,前2枚欧拉币之和为1513083232796311

求所有欧拉币之和。


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