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A263616
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Number of n-digit numbers whose square is a palindrome.
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1
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4, 3, 8, 5, 11, 6, 19, 14, 25, 18, 49, 31, 71, 46, 105, 71, 154, 101, 209, 132, 292, 182
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Number of terms in A002778 with exactly n digits.
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LINKS
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G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy] See page 95.
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EXAMPLE
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a(2) = 3 because there are three 2-digit numbers with palindromic squares: 11^2 = 121, 22^2 = 484, 26^2 = 676.
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MATHEMATICA
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Join[{4}, Table[Total[Table[If[PalindromeQ[n^2], 1, 0], {n, 10^x, 10^(x+1)-1}]], {x, 9}]] (* Harvey P. Dale, Apr 09 2019 *)
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PROG
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(Python)
from itertools import product
def pal(n): s = str(n); return s == s[::-1]
def a(n): return int(n==1) + sum(pal(i**2) for i in range(10**(n-1), 10**n))
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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