

A064021


Squares k^2 such that reverse(k)^2 = reverse(k^2), excluding squares of palindromes.


3



144, 169, 441, 961, 10404, 10609, 12544, 12769, 14884, 40401, 44521, 48841, 90601, 96721, 1004004, 1006009, 1022121, 1024144, 1026169, 1042441, 1044484, 1062961, 1212201, 1214404, 1216609, 1236544, 1238769, 1256641, 1258884, 1442401
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OFFSET

1,1


COMMENTS

Elements of A033294 that are not palindromes.  Walter Kehowski, May 22 2008
Subsequence of A035090.  M. F. Hasler, Mar 22 2011


REFERENCES

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 124, 127 (Rev. ed. 1997).


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 750 terms from Harry J. Smith)


FORMULA

{n = A000290(k) such that A004086(A000290(k)) = A000290(A004086(k)) and k is not in A002113}.  Jonathan Vos Post, May 02 2011
a(n) = A140212(n)^2.  Giovanni Resta, Jun 22 2018


EXAMPLE

1026169 is included because its square root, 1013, when reversed (i.e., 3101) and squared yields 9616201.
Squares < 10 and 121 = 11^2, 484 = 22^2, ... are not in the sequence, since they are the square of a palindrome.  M. F. Hasler, Mar 22 2011


MATHEMATICA

Cases[Range[2000]^2, k_ /; Mod[k, 10] != 0 && IntegerDigits[k] != Reverse[IntegerDigits[k]] && FromDigits[Reverse[IntegerDigits[Sqrt[k]]]]^2 == FromDigits[Reverse[IntegerDigits[k]]]] (* JeanFrançois Alcover, Mar 22 2011 *)


PROG

(PARI) Rev(x)= { local(d, r); r=0; while (x>0, d=x10*(x\10); x\=10; r=r*10 + d); return(r) }
{ n=0; for (m=1, 10^9, if (m%10==0, next); x=m^2; r=Rev(x); if (r==x, next); if (r==Rev(m)^2, write("b064021.txt", n++, " ", x); if (n==750, break)) ) } \\ Harry J. Smith, Sep 06 2009


CROSSREFS

Cf. A035124, A035123, A033294, A140212.
Sequence in context: A034289 A062917 A035090 * A156316 A323614 A245214
Adjacent sequences: A064018 A064019 A064020 * A064022 A064023 A064024


KEYWORD

nonn,base,nice


AUTHOR

Harvey P. Dale, Sep 18 2001


STATUS

approved



