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A002778
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Numbers whose square is a palindrome.
(Formerly M0907 N0342)
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11
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0, 1, 2, 3, 11, 22, 26, 101, 111, 121, 202, 212, 264, 307, 836, 1001, 1111, 2002, 2285, 2636, 10001, 10101, 10201, 11011, 11111, 11211, 20002, 20102, 22865, 24846, 30693, 100001, 101101, 110011, 111111, 200002, 798644, 1000001, 1001001
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A002779(n) = a(n)^2; A136522(A000290(a(n))) = 1. [Reinhard Zumkeller, Oct 11 2011]
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REFERENCES
| M. Keith, Classification and enumeration of palindromic squares, J. Rec. Math., 22 (No. 2, 1990), 124-132.
G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98.
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..485 (from P. De Geest)
P. De Geest, Palindromic Squares
Eric Weisstein's World of Mathematics, Palindromic Number.
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MATHEMATICA
| palsquareQ[n_] := (n2 = IntegerDigits[n^2]; n2 == Reverse[n2]); A002778 = {}; Do[ If[ palsquareQ[n], Print[n]; AppendTo[ A002778, n] ], {n, 0, 2*10^6}]; A002778 (* From Jean-François Alcover, Dec 01 2011 *)
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PROG
| (Haskell)
a002778 n = a002778_list !! (n-1)
a002778_list = filter ((== 1) . a136522 . (^ 2)) [0..]
-- Reinhard Zumkeller, Oct 11 2011
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CROSSREFS
| Cf. A002779, A002113.
Sequence in context: A097895 A023182 A049083 * A028816 A128921 A118595
Adjacent sequences: A002775 A002776 A002777 * A002779 A002780 A002781
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KEYWORD
| base,nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Patrick De Geest (pdg(AT)worldofnumbers.com).
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