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
KEYWORD
nonn,base
AUTHOR
Jean-François Alcover, Mar 08 2011
STATUS
approved