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%I #19 Feb 18 2024 13:19:39
%S 1,12,21,192,294,2536,2639,3903,4864,5342,6242,7302,7934,8023,9194,
%T 9711,12166,20719,22696,25964,51837,52453,60985,69186,69837,69984,
%U 76647,76992,82887,83814,84601,85257,87324,87603,87778,89208,98855,98918
%N Numbers m such that m^2 is an anagram of a Fibonacci number.
%C An anagram of a k-digit number is one of the k! permutations of the digits that does not begin with 0.
%H Michael S. Branicky, <a href="/A162391/b162391.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..417 from Chai Wah Wu)
%e 12^2 = 144 and 144 is F(12).
%e 192^2 = 36864 and 36864 is an anagram of F(24) = 46368.
%e 2536^2 = 6431296 and 6431296 is an anagram of F(31) = 1346269.
%t Table[Sqrt[#]&/@Select[FromDigits/@Permutations[IntegerDigits[ Fibonacci[ n]]],IntegerLength[#] == IntegerLength[Fibonacci[n]]&&IntegerQ[ Sqrt[ #]]&],{n,50}]//Flatten//Union (* _Harvey P. Dale_, Sep 15 2019 *)
%o (Python)
%o from math import isqrt
%o def agen(LIMIT): # generator of terms less than sqrt(LIMIT)
%o fibs = set()
%o f, g = 1, 2
%o while f <= LIMIT:
%o fibs.add("".join(sorted(str(f))))
%o f, g = g, f+g
%o r = s = 1
%o r = s = 1
%o while s <= LIMIT:
%o if "".join(sorted(str(s))) in fibs: yield r
%o r += 1
%o s = r*r
%o print(list(agen(10**10))) # _Michael S. Branicky_, Feb 18 2024
%Y Cf. A000045, A151820.
%K nonn,base
%O 1,2
%A _Claudio Meller_, Jul 02 2009
%E a(17)-a(38) from _Donovan Johnson_, Oct 11 2009
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