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A002779 Palindromic squares.
(Formerly M3371 N1358)
26
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

REFERENCES

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).

LINKS

Hans Havermann (via Feng Yuan), T. D. Noe (from P. De Geest) [to 485], Table of n, a(n) for n = 1..1940

Martianus Frederic Ezerman, Bertrand Meyer and Patrick Sole, On Polynomial Pairs of Integers, arXiv:1210.7593. 2012. - From N. J. A. Sloane, Nov 08 2012

P. De Geest, Palindromic Squares

W. R. Marshall, Palindromic Squares

Eric Weisstein's World of Mathematics, Palindromic Number.

F. Yuan, Palindromic Square Numbers

FORMULA

A010052(a(n)) * A136522(a(n)) = 1. - Reinhard Zumkeller, Oct 11 2011

EXAMPLE

676 is included because it is both a perfect square and a palindrome.

MATHEMATICA

PalindromeQ = ((# // IntegerDigits // Reverse // FromDigits) == #) &; Select[Table[n^2, {n, 0, 10000}], PalindromeQ] (* Herman Beeksma, Jul 14 2005 *)

pb10Q[n_]:=Module[{idn10=IntegerDigits[n, 10]}, idn10==Reverse[idn10]]; Select[Range[0, 20000]^2, pb10Q] (* Vincenzo Librandi, Jul 24 2014 *)

PROG

(Haskell)

a002779 n = a002778_list !! (n-1)

a002779_list = filter ((== 1) . a136522) a000290_list

-- Reinhard Zumkeller, Oct 11 2011

CROSSREFS

Cf. A000290, A002778, A002113, A057136, A136532, A010052.

Cf. A029734, A029738, A029806, A029983, A029985, A029987, A029989, A029991, A029993, A029995, A029997, A029999, A030074, A030075.

Sequence in context: A229971 A158642 A131760 * A028817 A057136 A048411

Adjacent sequences:  A002776 A002777 A002778 * A002780 A002781 A002782

KEYWORD

nonn,base,nice,easy

AUTHOR

N. J. A. Sloane, Apr 30 1991

STATUS

approved

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Last modified October 26 02:56 EDT 2014. Contains 248566 sequences.