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A064021
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Numbers n=k^2 such that reverse(k)^2 = reverse(k^2), excluding squares of palindromes.
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2
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Elements of A033294 that are not palindromes. - Walter A. Kehowski (wkehowski(AT)cox.net), May 22 2008
Subsequence of A035090. - M. F. Hasler, Mar 22 2011
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REFERENCES
| David Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 124, 127 (Rev. ed. 1997).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,750
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FORMULA
| {n = A000290(k) such that A004086(A000290(k)) = A000290(A004086(k)) and k is not in A002113}.[Jonathan Vos Post, May 2, 2011]
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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
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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-François Alcover, Mar 22 2011 *)
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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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 06 2009]
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CROSSREFS
| Cf. A035124, A035123.
Cf. A033294.
Sequence in context: A034289 A062917 A035090 * A156316 A165076 A165078
Adjacent sequences: A064018 A064019 A064020 * A064022 A064023 A064024
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KEYWORD
| nonn,base,nice
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AUTHOR
| Harvey P. Dale (hpd1(AT)nyu.edu), Sep 18 2001
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