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Search: id:A035519
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| A035519 |
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Rare numbers: n-r and n+r are both perfect squares, where r is reverse of n and n is non-palindromic. |
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3
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| 65, 621770, 281089082, 2022652202, 2042832002, 868591084757, 872546974178, 872568754178, 6979302951885, 20313693904202, 20313839704202, 20331657922202, 20331875722202, 20333875702202, 40313893704200
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Gupta, Shyam Sunder: Systematic computations of rare numbers, The Mathematics Education, Vol. XXXII, No. 3, Sept. 1998
R. K. Guy, Conway's RATS and other reversals, Unsolved Problems Column, American Math. Monthly, page 425, May 1989.
R. K. Guy, Unsolved problems come of Age, American Math. Monthly, page 908, Dec. 1989.
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LINKS
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Shyam Sunder Gupta, Rare Numbers
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EXAMPLE
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65 - 56 = 9 and 65 + 56 = 121 are both squares.
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MATHEMATICA
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r[n_]:=FromDigits[Reverse[IntegerDigits[n, 10]], 10]; f[n_]:=n!=r[n]&&IntegerQ[Sqrt[n-r[n]]]&&IntegerQ[Sqrt[n+r[n]]]; Timing[lst={}; Do[If[f[n], AppendTo[lst, n]], {n, 11, 15!}]; lst] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 10 2009]
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CROSSREFS
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Cf. A059755.
Sequence in context: A061688 A015072 A015039 this_sequence A059755 A157631 A138843
Adjacent sequences: A035516 A035517 A035518 this_sequence A035520 A035521 A035522
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KEYWORD
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nonn,base,nice
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AUTHOR
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Shyam Sunder Gupta (guptass(AT)rediffmail.com)
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EXTENSIONS
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There are 75 terms up to 10^19.
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