A162391 - OEIS

%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