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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 (list; graph; refs; listen; history; text; internal format)
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]]]] (* Jean-Fran├žois Alcover, Mar 22 2011 *)

PROG

(PARI) Rev(x)= { local(d, r); r=0; while (x>0, d=x-10*(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

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Last modified December 9 09:21 EST 2019. Contains 329877 sequences. (Running on oeis4.)