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A002779
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Palindromic squares.
(Formerly M3371 N1358)
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17
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0, 1, 4, 9, 121, 484, 676, 10201, 12321, 14641, 40804, 44944, 69696, 94249, 698896, 1002001, 1234321, 4008004, 5221225, 6948496, 100020001, 102030201, 104060401, 121242121, 123454321, 125686521, 400080004, 404090404, 522808225
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OFFSET
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1,3
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COMMENTS
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These are numbers that are both squares (see A000290) and palindromes (see A002113).
a(n) = A002778(n)^2; A136522(A000290(a(n))) = 1. [Reinhard Zumkeller, Oct 11 2011]
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REFERENCES
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Martianus Frederic Ezerman, Bertrand Meyer and Patrick Sole, On Polynomial Pairs of Integers, arXiv http://arxiv.org/abs/1210.7593. 2012. - From N. J. A. Sloane, Nov 08 2012
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
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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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FORMULA
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A010052(a(n))*A136522(a(n)) = 1. [Reinhard Zumkeller, Oct 11 2011]
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EXAMPLE
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676 is included because it is both a perfect square and a palindrome.
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MATHEMATICA
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PalindromeQ = ((# // IntegerDigits // Reverse // FromDigits) == #) &; Select[Table[n^2, {n, 0, 10000}], PalindromeQ] - Herman Beeksma (herman(AT)beeksma.nl), Jul 14 2005
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PROG
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(Haskell)
a002779 n = a002778_list !! (n-1)
a002779_list = filter ((== 1) . a136522) a000290_list
-- Reinhard Zumkeller, Oct 11 2011
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CROSSREFS
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Cf. A000290, A002778, A002113, A057136
Sequence in context: A115667 A158642 A131760 * A028817 A057136 A048411
Adjacent sequences: A002776 A002777 A002778 * A002780 A002781 A002782
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KEYWORD
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nonn,base,nice,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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