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A096913
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Numbers n such that (largest digit of n)^(smallest digit of n) + n is a square.
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0
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0, 13, 72, 80, 91, 120, 137, 163, 188, 251, 275, 281, 317, 321, 360, 388, 391, 440, 495, 527, 627, 840, 891, 960, 1023, 1088, 1148, 1151, 1288, 1363, 1437, 1520, 1591, 1674, 1680, 1757, 1841, 1927, 2024, 2113, 2208, 2303, 2365, 2400, 2464, 2491, 2565, 2600
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OFFSET
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1,2
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COMMENTS
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Conjecture: 0 and 3844 are the only squares in this sequence.
There are only finitely many squares in the sequence because for some square big enough the offset to the next square is greater than 9^9. Now, for each number d = (largest digit of n)^(smallest digit of n) we just have to walk through the squares, check if this square has the correct (largest digit of n)^(smallest digit of n) property and added d is also a square. I have done that search computation exhaustively (using a PARI program). There are no more squares. - Maon Wenders, Jun 02 2012
This sequence has infinitely many terms because there are infinitely many numbers b^2 - 1 that contain a zero in their decimal expansion. - T. D. Noe, Jul 20 2012
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LINKS
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Table of n, a(n) for n=1..48.
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EXAMPLE
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388 is in the sequence because 8^3 + 388 = 900 = 30^2.
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CROSSREFS
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Cf. A054054, A054055.
Sequence in context: A141989 A159512 A104132 * A026916 A106173 A094943
Adjacent sequences: A096910 A096911 A096912 * A096914 A096915 A096916
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Aug 17 2004
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STATUS
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approved
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