Mike_F Posted April 16, 2016 Report Share Posted April 16, 2016 14, 154, and 1196 all have a remarkable characteristic--one that no other integer below 2000 has. What is this characteristic? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted April 16, 2016 Report Share Posted April 16, 2016 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. 1 Quote Link to comment Share on other sites More sharing options...
0 Logophobic Posted April 17, 2016 Report Share Posted April 17, 2016 OEIS: A097227 Quote Link to comment Share on other sites More sharing options...
0 CaptainEd Posted April 18, 2016 Report Share Posted April 18, 2016 Bonanova, that's a remarkable numerological find! Quote Link to comment Share on other sites More sharing options...
0 Mike_F Posted April 18, 2016 Author Report Share Posted April 18, 2016 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... Quote Link to comment Share on other sites More sharing options...
0 CaptainEd Posted April 18, 2016 Report Share Posted April 18, 2016 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! Quote Link to comment Share on other sites More sharing options...
0 Mike_F Posted April 18, 2016 Author Report Share Posted April 18, 2016 Very true! Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted April 18, 2016 Report Share Posted April 18, 2016 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> Quote Link to comment Share on other sites More sharing options...
0 DejMar Posted April 26, 2016 Report Share Posted April 26, 2016 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. Quote Link to comment Share on other sites More sharing options...
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Mike_F
14, 154, and 1196 all have a remarkable characteristic--one that no other integer below 2000 has. What is this characteristic?
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