A030075
Squares which are palindromes in base 15.
Original entry on oeis.org
0, 1, 4, 9, 16, 64, 144, 256, 361, 1024, 1521, 4096, 5776, 16384, 20736, 51076, 58081, 65536, 73441, 96721, 204304, 218089, 228484, 232324, 331776, 511225, 817216, 929296, 1048576, 3055504, 3268864, 3489424, 5308416, 7033104
Offset: 1
8^2 = 64, which in base 15 is 44, and that's palindromic, so 64 is in the sequence.
9^2 = 81, which in base 15 is 56. Since that's not palindromic, 81 is not in the sequence.
Cf.
A002779,
A029734,
A029738,
A029806,
A029983,
A029985,
A029987,
A029989,
A029991,
A029993,
A029995,
A029997,
A029999,
A030074.
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N:= 10^10: # to get all entries <= N
count:= 0:
for x from 0 to floor(sqrt(N)) do
y:= x^2;
L:= convert(y,base,15);
if ListTools[Reverse](L) = L then
count:= count+1;
A[count]:= y;
fi
od:
seq(A[i],i=1..count); # Robert Israel, Jul 24 2014
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palQ[n_, b_:10] := Module[{idn = IntegerDigits[n, b]}, idn == Reverse[idn]]; Select[Range[0, 2700]^2, palQ[#, 15] &] (* Harvey P. Dale, Apr 23 2011 *)
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isok(n) = my(d=digits(n,15)); issquare(n) && (d == Vecrev(d)); \\ Michel Marcus, Oct 21 2016
A263610
Palindromes in base 4 which are also squares.
Original entry on oeis.org
0, 1, 121, 10201, 12321, 1002001, 1032301, 1223221, 100020001, 102030201, 103101301, 120202021, 10000200001, 10033233001, 1000002000001, 1002003002001, 1003010103001, 1021320231201, 1211130311121, 1212110112121, 1213332333121, 100000020000001, 100033323330001, 100331000133001
Offset: 1
A263609
Base-4 numbers whose square is a palindrome in base 4.
Original entry on oeis.org
0, 1, 11, 101, 111, 1001, 1013, 1103, 10001, 10101, 10121, 10331, 100001, 100133, 1000001, 1001001, 1001201, 1010301, 1100211, 1100323, 1101211, 10000001, 10001333, 10013201, 10031113, 100000001, 100010001, 100012001, 100103001, 100301113, 100332101, 101002101, 103231203, 110002011
Offset: 1
From _Mattew Bondar_, Mar 12 2021: (Start)
111_4 = 21_10, 21^2 = 441, 441_10 = 12321_4 (palindrome).
1013_4 = 71_10, 71^2 = 5041, 5041_10 = 1032301_4 (palindrome). (End)
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FromDigits /@ IntegerDigits[Select[Range[0, 2^17], PalindromeQ@ IntegerDigits[#^2, 4] &], 4] (* Michael De Vlieger, Mar 13 2021 *)
-
def decimal_to_quaternary(n):
if n == 0:
return '0'
b = ''
while n > 0:
b = str(n % 4) + b
n = n // 4
return b
x = 0
counter = 0
while True:
y = decimal_to_quaternary(x ** 2)
if y == y[::-1]:
print(int(decimal_to_quaternary(x)))
counter += 1
x += 1 # Mattew Bondar, Mar 10 2021