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A002779 Palindromic squares.
(Formerly M3371 N1358)
17
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

T. D. Noe, Table of n, a(n) for n = 1..485 (from P. De Geest)

P. De Geest, Palindromic Squares

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

Eric Weisstein's World of Mathematics, Palindromic Number.

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

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

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.

STATUS

approved

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Last modified April 20 16:29 EDT 2014. Contains 240807 sequences.