A323000 - OEIS

%I #38 Aug 30 2019 02:43:59

%S 1,1,0,1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,1,0,0,1,1,1,0,

%T 1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,

%U 0,0,0,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0

%N Digits of the 2-adic integer 3^(1/3).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/P-adic_number">p-adic number</a>

%F a(n) = (A322701(n+1) - A322701(n))/2^n.

%F a(n) = 0 if A322701(n)^3 - 3 is divisible by 2^(n+1), otherwise a(n) = 1.

%e Equals ...0100110111001111001000011111000101111011.

%o (PARI) a(n) = lift(sqrtn(3+O(2^(n+1)), 3))\2^n

%Y Cf. A322701.

%Y Digits of p-adic cubic roots:

%Y this sequence (2-adic, 3^(1/3));

%Y A323045 (2-adic, 5^(1/3));

%Y A323095 (2-adic, 7^(1/3));

%Y A323096 (2-adic, 9^(1/3));

%Y A290566 (5-adic, 2^(1/3));

%Y A290563 (5-adic, 3^(1/3));

%Y A309443 (5-adic, 4^(1/3));

%Y A319297, A319305, A319555 (7-adic, 6^(1/3));

%Y A321106, A321107, A321108 (13-adic, 5^(1/3)).

%K nonn,base

%O 0

%A _Jianing Song_, Aug 30 2019