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A029805
Numbers k such that k^2 is palindromic in base 8.
12
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
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
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
KEYWORD
nonn,base
STATUS
approved