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A085305
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Numbers such that first reversing digits and then squaring equals the result of first squaring and then reversing.
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6
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0, 1, 2, 3, 11, 12, 13, 21, 22, 31, 101, 102, 103, 111, 112, 113, 121, 122, 201, 202, 211, 212, 221, 301, 311, 1001, 1002, 1003, 1011, 1012, 1013, 1021, 1022, 1031, 1101, 1102, 1103, 1111, 1112, 1113, 1121, 1122, 1201, 1202, 1211, 1212, 1301, 2001, 2002, 2011
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Numbers (other than 0) that end in zero are excluded. - N. J. A. Sloane, Mar 20 2010
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Index entry for sequences related to reversing digits of squares
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FORMULA
| Solutions to rev[x^2]=rev[x]^2.
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EXAMPLE
| n=13 is here because 31^2=961=rev[169]=rev[13^2]=rev[rev[31]^2]
Number of solutions below 1000000 is 363.
Only digits {0,1,2,3} seem to arise.
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MATHEMATICA
| rt[x_] := tn[Reverse[IntegerDigits[x]]] Do[s=rt[n^2]; s1=rt[n]^2; If[Equal[s, s1]&&!Equal[Mod[n, 10], 0], Print[{n, s, rt[s1]}]], {n, 0, 1000000}]
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PROG
| a085305 n = a085305_list !! (n-1)
a085305_list = 0 : filter (\x -> x `mod` 10 > 0
&& a004086 (x^2) == (a004086 x)^2) [1..]
-- Reinhard Zumkeller, Jul 08 2011
(MAGMA) [0] cat [ m: n in [1..1810] | Reverse(Intseq(m^2)) eq Intseq(Seqint(Reverse(Intseq(m)))^2) where m is n+Floor((n-1)/9) ]; // Bruno Berselli, Jul 08 2011
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CROSSREFS
| Cf. A085306. See A061909 for another version.
Sequence in context: A130803 A007932 A035122 * A189818 A116032 A116029
Adjacent sequences: A085302 A085303 A085304 * A085306 A085307 A085308
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KEYWORD
| base,nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jun 27 2003
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