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 A263609 Base-4 numbers whose square is a palindrome in base 4. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..34. G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy] EXAMPLE 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) MATHEMATICA FromDigits /@ IntegerDigits[Select[Range[0, 2^17], PalindromeQ@ IntegerDigits[#^2, 4] &], 4] (* Michael De Vlieger, Mar 13 2021 *) PROG (Python) 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 CROSSREFS Cf. A002778, A029986, A263610, A029987. Sequence in context: A265528 A099821 A193415 * A333415 A264406 A057148 Adjacent sequences: A263606 A263607 A263608 * A263610 A263611 A263612 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Oct 22 2015 STATUS approved

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Last modified September 13 18:02 EDT 2024. Contains 375910 sequences. (Running on oeis4.)