A140212 Numbers n not a multiple of 10 such that reverse(n^2) = reverse(n)^2, but reverse(n) is different from n.

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

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 A108710

Adjacent sequences: A140209 A140210 A140211 * A140213 A140214 A140215

Keyword

nonn,base

Author

Jean-François Alcover, Mar 08 2011

Status

approved