A030075 Squares which are palindromes in base 15.

0, 1, 4, 9, 16, 64, 144, 256, 361, 1024, 1521, 4096, 5776, 16384, 20736, 51076, 58081, 65536, 73441, 96721, 204304, 218089, 228484, 232324, 331776, 511225, 817216, 929296, 1048576, 3055504, 3268864, 3489424, 5308416, 7033104

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..106

Patrick De Geest, Palindromic Squares in bases 2 to 17

Example

8^2 = 64, which in base 15 is 44, and that's palindromic, so 64 is in the sequence.
9^2 = 81, which in base 15 is 56. Since that's not palindromic, 81 is not in the sequence.

Maple

N:= 10^10: # to get all entries <= N
count:= 0:
for x from 0 to floor(sqrt(N)) do
    y:= x^2;
    L:= convert(y, base, 15);
  if ListTools[Reverse](L) = L then
     count:= count+1;
     A[count]:= y;
   fi
od:
seq(A[i], i=1..count); # Robert Israel, Jul 24 2014

Mathematica

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 *)

Prog

(PARI) isok(n) = my(d=digits(n, 15)); issquare(n) && (d == Vecrev(d)); \\ Michel Marcus, Oct 21 2016

Crossrefs

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

Sequence in context: A368891 A073723 A161493 * A296111 A038784 A038239

Adjacent sequences: A030072 A030073 A030074 * A030076 A030077 A030078

Keyword

base,nonn,changed

Author

Patrick De Geest

Status

approved