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Numbers whose cube is palindromic in base 7.
1

%I #29 Aug 11 2024 14:36:52

%S 0,1,2,4,8,16,50,100,200,344,688,1376,2402,4804,9608,16808,33616,

%T 67232,117650,235300,470600,823544,1647088,3294176,5764802,11529604,

%U 23059208,40353608,80707216,161414432,282475250,564950500,1129901000,1977326744,3954653488,7909306976

%N Numbers whose cube is palindromic in base 7.

%C Contains triples with base-7 digits 10^k1, 20^k2, 40^k4 for k >= 1, where ^ denotes repeated concatenation. - _Michael S. Branicky_, Aug 02 2022

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

%o (PARI) isok(k) = my(d=digits(k^3, 7)); 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, 7))

%o print(list(islice(agen(), 22))) # _Michael S. Branicky_, Aug 02 2022

%Y Cf. A046238.

%K nonn,base

%O 1,3

%A _Patrick De Geest_, May 15 1998

%E a(30)-a(36) from _Michael S. Branicky_, Aug 03 2022