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A162391
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Numbers m such that m^2 is an anagram of a Fibonacci number.
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2
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1, 12, 21, 192, 294, 2536, 2639, 3903, 4864, 5342, 6242, 7302, 7934, 8023, 9194, 9711, 12166, 20719, 22696, 25964, 51837, 52453, 60985, 69186, 69837, 69984, 76647, 76992, 82887, 83814, 84601, 85257, 87324, 87603, 87778, 89208, 98855, 98918
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OFFSET
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1,2
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COMMENTS
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An anagram of a k-digit number is one of the k! permutations of the digits that does not begin with 0.
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LINKS
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EXAMPLE
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12^2 = 144 and 144 is F(12).
192^2 = 36864 and 36864 is an anagram of F(24) = 46368.
2536^2 = 6431296 and 6431296 is an anagram of F(31) = 1346269.
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MATHEMATICA
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Table[Sqrt[#]&/@Select[FromDigits/@Permutations[IntegerDigits[ Fibonacci[ n]]], IntegerLength[#] == IntegerLength[Fibonacci[n]]&&IntegerQ[ Sqrt[ #]]&], {n, 50}]//Flatten//Union (* Harvey P. Dale, Sep 15 2019 *)
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PROG
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(Python)
from math import isqrt
def agen(LIMIT): # generator of terms less than sqrt(LIMIT)
fibs = set()
f, g = 1, 2
while f <= LIMIT:
fibs.add("".join(sorted(str(f))))
f, g = g, f+g
r = s = 1
r = s = 1
while s <= LIMIT:
if "".join(sorted(str(s))) in fibs: yield r
r += 1
s = r*r
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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