A064021 -id:A064021 - cp's OEIS frontend

A035124 Nonpalindromic cubes remaining cubic which written backwards: take the cube root of n, reverse its digits, cube that and the result is n with its digits reversed.

1033364331, 1334633301, 1003303631331, 1331363033001, 1000330036301331, 1003033061330301, 1003333697667631, 1030331603303001, 1030637669664331, 1331036300330001, 1334669667360301, 1367667963333001, 1000033000363001331, 1000303030604030301, 1000333036964367631

Offset: 1

Patrick De Geest, Nov 15 1998

Cubes with trailing zeros are excluded.

			1011^3 = 1033364331 -> 1334633301 = 1101^3.
1003333697667631 is included because its cube root, 100111, when reversed (i.e., 111001) and cubed yields 1367667963333001.

P. De Geest, Palindromic Cubes
Eric Weisstein's World of Mathematics, Cubic Number
Index entry for sequences related to reversing digits of squares

Cf. A035090, A035125, A064021, A319389.

isok(n) = {if (ispower(n, 3, &k), dn = digits(n); if (Vecrev(dn) != dn, dk = Vecrev(digits(k)); rk = subst(Pol(dk, x), x, 10); digits(rk^3) == Vecrev(dn);););} \\ Michel Marcus, Oct 04 2015

More terms from Seiichi Manyama, Sep 18 2018

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

Original entry on oeis.org

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

Jean-François Alcover, Mar 08 2011

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},...}

			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.

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

Cf. A064021. Subsequence of A035123.

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 ]

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

cp's OEIS Frontend

A035124 Nonpalindromic cubes remaining cubic which written backwards: take the cube root of n, reverse its digits, cube that and the result is n with its digits reversed.

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