9814072356 is 99066 squared, and is the eighty-seventh and largest square number using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 exactly once (sequence A036745 in OEIS).
More generally, it is also the largest distinct-digit perfect power being the 657th such number (A075309). Note that the digital root of both 9814072356 and 657 is 9.
It is the square of the third largest 5-digit strobogrammatic number (99866 and 99166 being larger).
It is also a member of A090516, the sequence of perfect powers where all neighbouring digits are distinct.
All the prime digits are adjacent 7,2,3,5 in a cycle, which is equal to the cycle {2357} of the natural order.
9814072356 is a permutation: of order 10 read left to right, and of order 6 ({9},{8},{2,3},{0,6,4,7,1,5}) read right to left.
In base 2 and 3 its last 6 digits are the same (100100).
See also
External links
References
- Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 159 and 165, 1979.
- David Wells, ed. Curious and Interesting Numbers 1988, page 192 and 193
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