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Numbers whose cube is palindromic in base 6.
1

%I #19 Aug 11 2024 14:36:45

%S 0,1,7,37,217,1297,7777,46657,279937,1679617,10077697,60466177,

%T 362797057,860627456,2176782337

%N Numbers whose cube is palindromic in base 6.

%C Note that '7777' is itself a palindrome, even a repdigit !

%C Next term is >10000000000. - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006

%H Patrick De Geest, <a href="https://www.worldofnumbers.com/nobase10pg4.htm">World!Of Numbers</a>, Palindromic cubes in bases 2 to 17.

%t For[i = 1, i < 1000000, i++, tmp = IntegerDigits[i^3, 6]; 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, 6)); 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(start=0): yield from (k for k in count(start) if ispal(k**3, 6))

%o print(list(islice(agen(), 10))) # _Michael S. Branicky_, Aug 02 2022

%Y Cf. A046236.

%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