A029805 Numbers k such that k^2 is palindromic in base 8.

0, 1, 2, 3, 6, 9, 11, 27, 65, 73, 79, 81, 83, 195, 219, 237, 366, 513, 543, 585, 697, 1094, 1539, 1755, 1875, 2910, 4097, 4161, 4225, 4477, 4617, 4681, 4727, 4891, 5267, 8698, 8730, 11841, 12291, 12483, 12675, 13065, 13851, 14673, 15021

Offset

1,3

Comments

The only powers of 2 in this sequence are 1 and 2. - Alonso del Arte, Feb 25 2017

Links

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

Patrick De Geest, Palindromic numbers beyond base 10

Example

3 is in the sequence because 3^2 = 9 = 11 in base 8, which is a palindrome.
4 is not in the sequence because 4^2 = 16 = 20 in base 8, which is not a palindrome.

Mathematica

palQ[n_, b_:10] := Module[{idn = IntegerDigits[n, b]}, idn == Reverse[idn]]; Select[Range[0, 16000], palQ[#^2, 8] &] (* Harvey P. Dale, May 19 2012 *)

Prog

(Python)
from itertools import count, islice
def A029805_gen(): # generator of terms
    return filter(lambda k: (s:=oct(k**2)[2:])[:(t:=(len(s)+1)//2)]==s[:-t-1:-1], count(0))
A029805_list = list(islice(A029805_gen(), 20)) # Chai Wah Wu, Jun 23 2022

Crossrefs

Cf. A000290, A002441, A007094.

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), this sequence (b=8), A029994 (b=9), A002778 (b=10), A029996 (b=11), A029737 (b=12), A029998 (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

Sequence in context: A018537 A018331 A032704 * A082007 A064417 A191981

Adjacent sequences: A029802 A029803 A029804 * A029806 A029807 A029808

Keyword

nonn,base

Author

Patrick De Geest

Status

approved