Saturday, 5 December 2015

Permutations of Digits 1 to 5


Even though the number 24351 doesn't seem to have much mathematical significance, it nonetheless should not pass unnoticed because the digits that comprise it are a permutation of the first five digits: 1, 2, 3, 4 and 5. The occurrences of this thus far have been:

12345, 12354, 12435, 12453, 12534, 12543, 13245, 13254, 13425, 13452, 13524, 13542, 14235, 14253, 14325, 14352, 14523, 14532, 15234, 15243, 15324, 15342, 15423, 15432, 21345, 21354, 21435, 21453, 21534, 21543, 23145, 23154, 23415, 23451, 23514, 23541, 24135, 24153, 24315, 24351

Thus it can be seen that 24351 is the fortieth such occurrence and because the sum of the first five digits is 15, all of these numbers are divisible by 3 and thus none are prime. The first occurrence (12345) took place on Thursday, January 20, 1983 when I was in England with Ali and Tara. I was still 33 years of age at that time, half my current age. The continuation will be:

24513, 24531, 25134, 25143, 25314, 25341, 25413, 25431, 31245, ...

The jump from 25431 to 31245 is a big one with the latter falling on Thursday, October 19, 2034. If I make it that far, I'll be over 85 years old.

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