Today, January 11th 2016, I'm 24389 days old and what's special is that this number is 29 cubed or 29 x 29 x 29. Days like this are rare. For example, \(28^3 \) or 21592 occurred on May 10th 2009 and \(30^3 \) or 27000 will occur on March 6th 2023. Cubes of prime numbers are even rarer of course. The prime preceding 29 is 23 and \(23^3 \) or 12167 occurred on July 26th 1982. The prime following 29 is 31 and \( 31^3 \) or 29791 will occur on October 26th 2030 when I'm 81 years of age (if I make it that far).
24389 has a surprisingly large number of entries in the Online Encyclopaedia of Integer Sequences (OEIS), 174 in fact which is unusual for a composite number of this magnitude. The first entry is for OEIS A000578: the cubes \( a(n) = n^3 \). The sequence, up to 24389 when n=29, looks like this:
0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389
The next entry is OEIS A030078: cubes of primes. The sequence, up to 24389, is: 8, 27, 125, 343, 1331, 2197, 4913, 6859, 12167, 24389.
From WolframAlpha, we find that 24389 is also a cube that is expressible as the sum of two squares in two different ways:
\(24389 = 58^2+145^2 = 65^2+142^2 \)
Additionally, we find that 24389 is the hypotenuse of a primitive Pythagorean triple:
\(24389^2 = 15939^2+18460^2 \). So, all in all, an interesting number.
24389 has a surprisingly large number of entries in the Online Encyclopaedia of Integer Sequences (OEIS), 174 in fact which is unusual for a composite number of this magnitude. The first entry is for OEIS A000578: the cubes \( a(n) = n^3 \). The sequence, up to 24389 when n=29, looks like this:
0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389
The next entry is OEIS A030078: cubes of primes. The sequence, up to 24389, is: 8, 27, 125, 343, 1331, 2197, 4913, 6859, 12167, 24389.
From WolframAlpha, we find that 24389 is also a cube that is expressible as the sum of two squares in two different ways:
\(24389 = 58^2+145^2 = 65^2+142^2 \)
Additionally, we find that 24389 is the hypotenuse of a primitive Pythagorean triple:
\(24389^2 = 15939^2+18460^2 \). So, all in all, an interesting number.
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