A162391 Numbers m such that m^2 is an anagram of a Fibonacci number.

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

Cf. A000045, A151820.

Sequence in context: A260275 A001292 A292523 * A114015 A065439 A214218

Adjacent sequences: A162388 A162389 A162390 * A162392 A162393 A162394

Keyword

nonn,base

Author

Claudio Meller, Jul 02 2009

Extensions

a(17)-a(38) from Donovan Johnson, Oct 11 2009

Status

approved