A322933 - OEIS

%I #17 Aug 17 2019 03:13:56

%S 7,2,6,6,2,7,7,2,0,6,5,6,7,3,5,6,1,5,6,1,0,0,2,4,6,1,5,0,4,3,3,4,3,3,

%T 0,5,2,5,4,4,5,2,7,5,2,7,2,1,4,5,7,5,7,0,2,7,0,1,3,2,4,7,6,5,1,1,2,4,

%U 2,0,7,2,5,4,0,4,7,0,4,3,5,5,1,3,4,4,6,1,7,7,3,5,3,6,6,5,7,5,0,6

%N Digits of the 8-adic integer 7^(1/3).

%C The octal version of A225405.

%H Seiichi Manyama, <a href="/A322933/b322933.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hensel%27s_lemma">Hensel's Lemma</a>.

%F Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 5 * (b(n-1)^3 - 7) mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n. - _Seiichi Manyama_, Aug 14 2019

%e 56027726627^3 == 7 (mod 8^11) in octal.

%o (PARI) N=100; Vecrev(digits(lift((7+O(2^(3*N)))^(1/3)), 8), N) \\ _Seiichi Manyama_, Aug 14 2019

%o (Ruby)

%o def A322933(n)

%o   ary = [7]

%o   a = 7

%o   n.times{|i|

%o     b = (a + 5 * (a ** 3 - 7)) % (8 ** (i + 2))

%o     ary << (b - a) / (8 ** (i + 1))

%o     a = b

%o   }

%o   ary

%o end

%o p A322933(100) # _Seiichi Manyama_, Aug 14 2019

%Y Cf. A225405 (decimal version), A322931, A322932.

%K nonn,base,easy

%O 0,1

%A _Patrick A. Thomas_, Dec 31 2018