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Search: id:A082994
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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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1
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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
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OFFSET
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1,1
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COMMENT
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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
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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
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a(5) = 867 because 867 * 768 = 665856 = 816^2.
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CROSSREFS
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Sequence in context: A011817 A035882 A061831 this_sequence A127350 A158253 A128392
Adjacent sequences: A082991 A082992 A082993 this_sequence A082995 A082996 A082997
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KEYWORD
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base,nonn,new
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), May 29 2003
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