A029733 Numbers k such that k^2 is palindromic in base 16.

0, 1, 2, 3, 17, 34, 257, 273, 289, 305, 319, 514, 530, 546, 773, 1377, 4097, 4369, 4641, 8194, 8254, 8466, 8734, 9046, 51629, 65537, 65793, 66049, 66305, 69649, 69905, 70161, 70417, 73505, 73761, 74017, 74273, 76879, 92327, 131074

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..100
• Patrick De Geest, Palindromic Squares in bases 2 to 17

Crossrefs

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), A029992 (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), this sequence (b=16), A118651 (b=17).

Programs

Mathematica

n2palQ[n_]:=Module[{id=IntegerDigits[n^2,16]},id==Reverse[id]]; Select[ Range[ 0,150000],n2palQ] (* Harvey P. Dale, Mar 31 2018 *)

Python

from itertools import count, islice
def A029733_gen(): # generator of terms
    return filter(lambda k: (s:=hex(k**2)[2:])[:(t:=(len(s)+1)//2)]==s[:-t-1:-1],count(0))
A029733_list = list(islice(A029733_gen(),20)) # Chai Wah Wu, Jun 23 2022