A234472 Numbers that when raised to the fourth power and written backwards give squares.

0, 1, 10, 11, 100, 101, 110, 1000, 1001, 1010, 1100, 10000, 10001, 10010, 10100, 11000, 100000, 100001, 100010, 100100, 101000, 110000, 1000000, 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 10000000, 10000001, 10000010, 10000100, 10001000, 10010000

Offset: 1

Author

Colin Barker, Dec 26 2013

Keywords

• nonn
• base
• nice

Comments

It seems that the numbers contain only the digits 0 and 1, and that the reversed fourth power and the square root of the reversed fourth power are both palindromes.

If the above comment is correct, and also if (as it appears) no more than two ones are among the digits of any term, this Mathematica program quickly generates the terms of the sequence: Flatten[Table[Select[ FromDigits/@Permutations[PadRight[PadRight[{},k,1],8,0]],IntegerQ[ Sqrt[ IntegerReverse[#^4]]]&],{k,0,2}]]//Sort - Harvey P. Dale, May 05 2020

Examples

			101 is in the sequence because 101^4 = 104060401 and 104060401 = 10201^2.
110 is in the sequence because 110^4 = 146410000 and 14641 = 121^2.
		

Crossrefs

Cf. A102859, A043681.

Programs

Magma

[n: n in [0..10^7] | IsSquare(Seqint(Reverse(Intseq(n^4))))]; // Bruno Berselli, Dec 27 2013

Mathematica

Select[Range[0,10^7],IntegerQ[Sqrt[IntegerReverse[#^4]]]&] (* Harvey P. Dale, May 05 2020 *)

PARI

revint(n) = m=n%10; n\=10; while(n>0, m=m*10+n%10; n\=10); m
s=[]; for(i=0, 1000000, if(issquare(revint(i^4)), s=concat(s, i))); s

Python

from itertools import count, islice
from sympy import integer_nthroot
def A234472_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:integer_nthroot(int(str(n**4)[::-1]),2)[1], count(max(startvalue,0)))
A234472_list = list(islice(A234472_gen(),10)) # Chai Wah Wu, Nov 18 2022