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A082994
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Numbers n such that n*reverse(n) is a square, n and reverse(n) are not equal and n and reverse(n) are both not squares.
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288, 528, 768, 825, 867, 882, 1584, 2178, 4851, 8712, 10989, 13104, 14544, 15984, 20808, 21978, 26208, 27648, 27848, 36828, 40131, 44541, 48139, 48951, 49686, 57399, 68694, 80262, 80802, 82863, 84672, 84872, 87912, 93184, 98901, 99375
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| These terms are counterexamples to the following conjecture given in the Ogilvy-Anderson reference: "When an integer and its reversal are unequal, their product is never a square except when both are squares." Also, this sequence excludes terms like 2200, i.e. 2200*22 = 48400.
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REFERENCES
| Author?, "Conjecture on reversals," American Mathematical Monthly, vol. 64 (1957), p. 434, E-1243.
C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, NY. (1966), pp. 88-89.
J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 82-83. ASIN: B002ACVZ6O [From Jason Earls (zevi_35711(AT)yahoo.com), Nov 22 2009]
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EXAMPLE
| a(5) = 867 because 867 * 768 = 665856 = 816^2.
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CROSSREFS
| Sequence in context: A011817 A035882 A061831 * A127350 A158253 A179646
Adjacent sequences: A082991 A082992 A082993 * A082995 A082996 A082997
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KEYWORD
| base,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), May 29 2003
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