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%I #21 Apr 05 2021 04:09:01
%S 0,1,11,101,111,1001,1013,1103,10001,10101,10121,10331,100001,100133,
%T 1000001,1001001,1001201,1010301,1100211,1100323,1101211,10000001,
%U 10001333,10013201,10031113,100000001,100010001,100012001,100103001,100301113,100332101,101002101,103231203,110002011
%N Base-4 numbers whose square is a palindrome in base 4.
%H G. J. Simmons, <a href="/A002778/a002778.pdf">On palindromic squares of non-palindromic numbers</a>, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]
%e From _Mattew Bondar_, Mar 12 2021: (Start)
%e 111_4 = 21_10, 21^2 = 441, 441_10 = 12321_4 (palindrome).
%e 1013_4 = 71_10, 71^2 = 5041, 5041_10 = 1032301_4 (palindrome). (End)
%t FromDigits /@ IntegerDigits[Select[Range[0, 2^17], PalindromeQ@ IntegerDigits[#^2, 4] &], 4] (* _Michael De Vlieger_, Mar 13 2021 *)
%o (Python)
%o def decimal_to_quaternary(n):
%o if n == 0:
%o return '0'
%o b = ''
%o while n > 0:
%o b = str(n % 4) + b
%o n = n // 4
%o return b
%o x = 0
%o counter = 0
%o while True:
%o y = decimal_to_quaternary(x ** 2)
%o if y == y[::-1]:
%o print(int(decimal_to_quaternary(x)))
%o counter += 1
%o x += 1 # _Mattew Bondar_, Mar 10 2021
%Y Cf. A002778, A029986, A263610, A029987.
%K nonn,base
%O 1,3
%A _N. J. A. Sloane_, Oct 22 2015
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