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A162391
Numbers m such that m^2 is an anagram of a Fibonacci number.
2
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
OFFSET
1,2
COMMENTS
An anagram of a k-digit number is one of the k! permutations of the digits that does not begin with 0.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..417 from Chai Wah Wu)
EXAMPLE
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.
MATHEMATICA
Table[Sqrt[#]&/@Select[FromDigits/@Permutations[IntegerDigits[ Fibonacci[ n]]], IntegerLength[#] == IntegerLength[Fibonacci[n]]&&IntegerQ[ Sqrt[ #]]&], {n, 50}]//Flatten//Union (* Harvey P. Dale, Sep 15 2019 *)
PROG
(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
print(list(agen(10**10))) # Michael S. Branicky, Feb 18 2024
CROSSREFS
Sequence in context: A260275 A001292 A292523 * A114015 A065439 A214218
KEYWORD
nonn,base
AUTHOR
Claudio Meller, Jul 02 2009
EXTENSIONS
a(17)-a(38) from Donovan Johnson, Oct 11 2009
STATUS
approved