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A202386
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Nonpalindromic numbers m such that the difference between the square of m and the square of the reversal of m is itself a perfect square. Numbers ending in 0 are excluded.
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5
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65, 5625, 6565, 50721, 65065, 71555, 75515, 84295, 541063, 557931, 650065, 650606, 656565, 699796, 809325, 827372, 934065, 2855182, 4637061, 4854634, 5791775, 5883141, 5951693, 6129084, 6500065, 6731076, 6752626, 6791774, 7768827, 8084505, 9349065
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OFFSET
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1,1
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COMMENTS
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This sequence is infinite because 65*10^k + 65 is a term for all k > 1.
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1996, p. 147.
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LINKS
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Giovanni Resta, Table of n, a(n) for n = 1..200
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EXAMPLE
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5625 belongs to this sequence because 5625^2 - 5265^2 = 1980^2.
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MATHEMATICA
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lst = {}; Do[a = n^2; b = FromDigits[Reverse[IntegerDigits[n]]]^2; If[MatchQ[Sqrt[a - b], _Integer] && ! a == b, AppendTo[lst, n]], {n, 85000}]; Select[lst, ! Mod[#, 10] == 0 &]
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PROG
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(PARI) isok(m) = my(r=fromdigits(Vecrev(digits(m)))); (r != m) && (m % 10) && issquare(m^2 - r^2); \\ Michel Marcus, Feb 27 2020
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CROSSREFS
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Cf. A068536, A000290.
Sequence in context: A110900 A084272 A146756 * A294955 A115432 A116104
Adjacent sequences: A202383 A202384 A202385 * A202387 A202388 A202389
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KEYWORD
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nonn,base
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AUTHOR
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Arkadiusz Wesolowski, Dec 18 2011
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EXTENSIONS
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Name clarified by Michel Marcus, Feb 27 2020
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STATUS
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approved
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