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A234472 Numbers that when raised to the fourth power and written backwards give squares. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

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.

MATHEMATICA

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

PROG

(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

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

CROSSREFS

Cf. A102859, A043681.

Sequence in context: A136831 A204009 A043681 * A139707 A139709 A221714

Adjacent sequences:  A234469 A234470 A234471 * A234473 A234474 A234475

KEYWORD

nonn,base,nice

AUTHOR

Colin Barker, Dec 26 2013

STATUS

approved

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Last modified July 4 02:56 EDT 2020. Contains 335436 sequences. (Running on oeis4.)