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%I #32 Aug 02 2022 09:21:07
%S 0,1,5,17,65,257,1025,4097,16385,65537,262145,1048577,4194305,
%T 16777217,67108865,268435457,1073741825,4294967297
%N Numbers whose cube is palindromic in base 4.
%C No number less than 10^8 has a cube that is palindromic in base 2 or base 3.
%C Next term exceeds 10000000000. - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/index.html">World!Of Numbers</a>
%F It seems that for n>=2, a(n)=4^(n-1)+1. - _Benoit Cloitre_, Dec 07 2003
%t For[i = 1, i < 1000000, i++, tmp = IntegerDigits[i^3, 4]; If[tmp == Reverse[tmp], Print[i]] ]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006 *)
%o (PARI) isok(k) = my(d=digits(k^3,4)); Vecrev(d) == d; \\ _Michel Marcus_, Aug 02 2022
%o (Python)
%o from itertools import count, islice
%o from sympy.ntheory import is_palindromic as ispal
%o def agen(startk=0): yield from (k for k in count(startk) if ispal(k**3, 4))
%o print(list(islice(agen(), 12))) # _Michael S. Branicky_, Aug 02 2022
%Y Cf. A046232.
%Y Cf. A052539. - _R. J. Mathar_, Oct 13 2008
%K nonn,more,base
%O 1,3
%A _Patrick De Geest_, May 15 1998
%E More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006, corrected Nov 01 2006