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A030075 Squares which are palindromes in base 15.

%I A030075 #23 Feb 10 2025 20:03:41
%S A030075 0,1,4,9,16,64,144,256,361,1024,1521,4096,5776,16384,20736,51076,
%T A030075 58081,65536,73441,96721,204304,218089,228484,232324,331776,511225,
%U A030075 817216,929296,1048576,3055504,3268864,3489424,5308416,7033104
%N A030075 Squares which are palindromes in base 15.
%H A030075 Vincenzo Librandi, <a href="/A030075/b030075.txt">Table of n, a(n) for n = 1..106</a>
%H A030075 Patrick De Geest, <a href="https://www.worldofnumbers.com/nobase10pg2.htm">Palindromic Squares in bases 2 to 17</a>
%e A030075 8^2 = 64, which in base 15 is 44, and that's palindromic, so 64 is in the sequence.
%e A030075 9^2 = 81, which in base 15 is 56. Since that's not palindromic, 81 is not in the sequence.
%p A030075 N:= 10^10: # to get all entries <= N
%p A030075 count:= 0:
%p A030075 for x from 0 to floor(sqrt(N)) do
%p A030075     y:= x^2;
%p A030075     L:= convert(y,base,15);
%p A030075   if ListTools[Reverse](L) = L then
%p A030075      count:= count+1;
%p A030075      A[count]:= y;
%p A030075    fi
%p A030075 od:
%p A030075 seq(A[i],i=1..count); # _Robert Israel_, Jul 24 2014
%t A030075 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 *)
%o A030075 (PARI) isok(n) = my(d=digits(n,15)); issquare(n) && (d == Vecrev(d)); \\ _Michel Marcus_, Oct 21 2016
%Y A030075 Cf. A002779, A029734, A029738, A029806, A029983, A029985, A029987, A029989, A029991, A029993, A029995, A029997, A029999, A030074.
%K A030075 base,nonn
%O A030075 1,3
%A A030075 _Patrick De Geest_