

A140212


Numbers n not a multiple of 10 such that reverse(n^2) = reverse(n)^2, but reverse(n) is different from n.


2



12, 13, 21, 31, 102, 103, 112, 113, 122, 201, 211, 221, 301, 311, 1002, 1003, 1011, 1012, 1013, 1021, 1022, 1031, 1101, 1102, 1103, 1112, 1113, 1121, 1122, 1201, 1202, 1211, 1212, 1301, 2001, 2011, 2012, 2021, 2022, 2101, 2102, 2111, 2121, 2201, 2202, 2211, 3001, 3011, 3101, 3111
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OFFSET

1,1


COMMENTS

This sequence is similar to A035123 but excludes integers such as 33 or 99 or 3168, because they don't meet the commutativity criterion reverse(n^2) = (reverse(n))^2.
Compare for instance:
{reverse(3168^2), reverse(3168)^2} > {42263001, 74183769}
with:
{reverse(3111^2), reverse(3111)^2} > {1238769, 1238769}
Terms can be matched by pairs:
{{12, 21}, {13, 31}, {102, 201}, {103, 301}, {112, 211}, {113, 311}, {122, 221}, {1002, 2001}, {1003, 3001}, {1011, 1101}, {1012, 2101}, {1013, 3101}, {1021, 1201}, {1022, 2201}, {1031, 1301}, {1102, 2011}, {1103, 3011}, {1112, 2111}, {1113, 3111}, {1121, 1211}, {1122, 2211}, {1202, 2021}, {1212, 2121}, {2012, 2102}, {2022, 2202},...}


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 300 terms from Vincenzo Librandi)


FORMULA

a(n)^2 = A064021(n).  Giovanni Resta, Jun 22 2018


EXAMPLE

113 belongs to the sequence because sqrt(reverse(113^2)) = 311, which is 113 written backwards, whereas 99 does not: sqrt(reverse(99^2)) = 33.


MATHEMATICA

r[n_] := FromDigits[Reverse[IntegerDigits[n]]];
Cases[Range[10000], n_ /; Mod[n, 10] != 0 && r[n^2] != n^2 && r[n^2] == r[n]^2 ]


CROSSREFS

Cf. A064021. Subsequence of A035123.
Sequence in context: A057488 A105733 A035123 * A123132 A050840 A118068
Adjacent sequences: A140209 A140210 A140211 * A140213 A140214 A140215


KEYWORD

nonn,base


AUTHOR

JeanFrançois Alcover, Mar 08 2011


STATUS

approved



