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Mike_F

3 remarkable numbers

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I'll bet this is not the answer you're looking for, but it does qualify as a remarkable matchup:

Spoiler

Last season, Ohio prep football star (American style) Alden Hill wore jersey number 14 and carried the ball 154 times for 1,196 yards.

 

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Yes, it turns out that the answer is Googlable... I like to call these "factorially self-referential" numbers, in that they refer to their own prime factors:

14 = 1st prime x 4th prime

154 = 1st prime x 5th prime x 4th prime

1196 = 1st x 1st x 9th x 6th

2127 = 2nd x 127th

61411 = 61st x 4th x 11th

66079 = 6th x 6th x 7th x 9th

172482 = 1st x 7th x 24th x 8th x 2nd

223227 = 2nd x 232nd x 2nd x 7th

279174 = 2nd x 7th x 9th x 1st x 7th x 4th

291318 = 2nd x 9th x 1st x 318th

 

I think this is it for integers below 1 million. Perhaps others will want to look for more -- or just let this bit of silliness stop...

 

 

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Mike, I agree that is interestingly Googlable. But my comment was that Bonanova was able to come up with something using exactly those numbers in an entirely different context. Both of these findings are remarkable!

 

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The puzzle is interesting, especially for those who are into number theory.

Last week I looked at this puzzle and decided I would not be able to find the connection among the numbers. So I searched OEIS out of curiosity. For some reason I didn't find it. (Strange.) Next I Googled the numbers themselves, and that turned up the football reference.

<moderator hat on>

I agree with Mike's sentiments. The Forum is for solving puzzles; it's not an Internet scavenger hunt. If you can't solve it, say so and maybe start a (spoilered) group effort. Or ask the OP for a clue.

The spoiler function permits multiple users to have a go at solving a puzzle. So solutions belong there. (Even funny ones about football.)

<moderator hat off>

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It can be argued that 2, 3, 5, and 7 are members of the sequence. Where the decimal expansion of n is 1, k = 1, and thus the number remains simply the prime. The integer sequence A097227 should, with the exclusion of these terms, state that the there are a minimum of two digits in each term, i.e., k > 1. Though the OEIS tries to be thoroughly correct, it is not always.

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