Still here at the van der Poorten memorial conference in Newcastle, Australia. The following problem occurred to me:
What is special about the integer 2007986541?
The labels for the post may give some hints.
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Jeffrey Shallit
Recurrent thoughts about mathematics, science, politics, music, religion, and
Recurrent thoughts about mathematics, science, politics, music, religion, and
Recurrent thoughts about mathematics, science, politics, music, religion, and
Recurrent thoughts about ....
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Jeffrey Shallit
American mathematician, professor of computer science at a major Canadian university, & skeptic.
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Recursivity
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10 comments:
It lacks a '3'
The sum of the digits is the answer to the epoch question - What is the meaning of life the universe and everything -
Okay a bit more, its divisible by the sum of its digits as well.
It's a Harshad number. These numbers give a person joy.
It is NOT divisible by the sum of its digits! The sum of its digits is 42 and its prime factorization is 3 x 11 x 60848077. I don't see what is special about it yet.
Hint: try the sum of digits in some prime bases.
Miranda's a real googlin' fool! Knows no more or less than google can provide.
Sum of digits is 21 in bases 2,3,5,7,11,13. (So it's Harshad in bases 3 and 11, for what that's worth.)
Naive searching quickly finds that 1386, 1387, 485353 have digit-sums the same in bases 2,3,5,7,11. Is 2007986541 the smallest such number when base 13 is included too? (My slow-and-dirty searching program says there are none below 20,000,000. I was too impatient to let it run >100x longer.)
Right, it's the smallest integer > 1 whose sum of digits in bases 2,3,5,7,11, and 13 is the same.
"Knows no ... less than google can provide."
Thanks for the compliment!!
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