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

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..100

Patrick De Geest, Palindromic numbers beyond base 10

Mathematica

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

Prog

(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

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).

Sequence in context: A193051 A217688 A263570 * A153686 A042137 A067976

Adjacent sequences: A029730 A029731 A029732 * A029734 A029735 A029736

Keyword

nonn,base

Author

Patrick De Geest

Status

approved