A030075 - OEIS

%I #21 Oct 21 2016 00:35:39

%S 0,1,4,9,16,64,144,256,361,1024,1521,4096,5776,16384,20736,51076,

%T 58081,65536,73441,96721,204304,218089,228484,232324,331776,511225,

%U 817216,929296,1048576,3055504,3268864,3489424,5308416,7033104

%N Squares which are palindromes in base 15.

%H Vincenzo Librandi, <a href="/A030075/b030075.txt">Table of n, a(n) for n = 1..106</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/square.htm">Palindromic Squares</a>

%e 8^2 = 64, which in base 15 is 44, and that's palindromic, so 64 is in the sequence.

%e 9^2 = 81, which in base 15 is 56. Since that's not palindromic, 81 is not in the sequence.

%p N:= 10^10: # to get all entries <= N

%p count:= 0:

%p for x from 0 to floor(sqrt(N)) do

%p     y:= x^2;

%p     L:= convert(y,base,15);

%p   if ListTools[Reverse](L) = L then

%p      count:= count+1;

%p      A[count]:= y;

%p    fi

%p od:

%p seq(A[i],i=1..count); # _Robert Israel_, Jul 24 2014

%t 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 (PARI) isok(n) = my(d=digits(n,15)); issquare(n) && (d == Vecrev(d)); \\ _Michel Marcus_, Oct 21 2016

%Y Cf. A002779, A029734, A029738, A029806, A029983, A029985, A029987, A029989, A029991, A029993, A029995, A029997, A029999, A030074.

%K base,nonn

%O 1,3

%A _Patrick De Geest_