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A358984
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The number of n-digit numbers k such that k + digit reversal of k (A056964) is a square.
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1
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3, 8, 19, 0, 169, 896, 1496, 3334, 21789, 79403, 239439, 651236, 1670022, 3015650, 27292097, 55608749, 234846164, 366081231, 2594727780, 6395506991
(list;
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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 of A061230 which are n digits long.
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LINKS
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EXAMPLE
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a(1) = 3 because there are 3 single-digit numbers: 0, 2, 8 such that b + b = m^2, for example, 8 + 8 = 16 = 4^2;
a(2) = 8 because there are 8 two-digit numbers: 29, 38, 47, 56, 65, 74, 83, 92 such that bc + cb = m^2, for example, 29 + 92 = 121 = 11^2.
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MATHEMATICA
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a[n_]:=Length[Select[Table[k, {k, 10^(n-1), 10^n-1}], IntegerQ[Sqrt[#+FromDigits[Reverse[IntegerDigits[#]]]]]&]]; Array[a, 10] (* Stefano Spezia, Dec 09 2022 *)
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PROG
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(Python)
from math import isqrt
def s(n): return isqrt(n)**2 == n
def c(n): return s(n + int(str(n)[::-1]))
def a(n): return 3 if n == 1 else sum(1 for k in range(10**(n-1), 10**n) if c(k))
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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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