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%I #23 Sep 08 2022 08:44:50
%S 0,1,2,4,8,10,11,20,32,40,50,57,64,80,160,200,344,400,500,550,557,730,
%T 1000,1376,1432,1892,2402,2451,2500,2752,2801,3440,3784,3902,5101,
%U 5266,6880,8296,9460,9608,9804,16808,17200,19216,19608,22693
%N Numbers k such that k^2 is palindromic in base 7.
%H Marius A. Burtea, <a href="/A029992/b029992.txt">Table of n, a(n) for n = 1..237</a>
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/square.htm">Palindromic Squares</a>
%e 8^2 = 64, which is 121 in base 7, and since that's palindromic, 8 is in the sequence.
%e 9^2 = 81, which is 144 in base 7, but since that's not palindromic, 9 is not in the sequence.
%t Select[Range[0, 16806], IntegerDigits[#^2, 7] == Reverse[IntegerDigits[#^2, 7]] &] (* _Alonso del Arte_, Jan 21 2020 *)
%o (Scala) (0 to 16806).filter(n => Integer.toString(n * n, 7) == Integer.toString(n * n, 7).reverse) // _Alonso del Arte_, Jan 21 2020
%o (Magma) [k:k in [0..23000]| Seqint(Intseq(k^2,7)) eq Seqint(Reverse(Intseq(k^2,7)))]; // _Marius A. Burtea_, Jan 22 2020
%Y Cf. A002440 (squares written in base 7), A007093.
%Y Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), A029986 (b=4), A029988 (b=5), A029990 (b=6), this sequence (b=7), A029805 (b=8), A029994 (b=9), A002778 (b=10), A029996 (b=11), A029737 (b=12), A029998 (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).
%K nonn,base
%O 1,3
%A _Patrick De Geest_