A225405 - OEIS

%I #19 Aug 13 2019 08:12:29

%S 3,4,5,1,5,0,7,1,2,2,2,4,4,2,9,6,0,7,3,5,4,5,8,8,8,0,4,1,8,5,1,4,0,0,

%T 6,1,3,5,4,4,8,1,3,7,4,0,7,4,8,5,5,1,6,7,4,5,5,0,0,4,9,0,4,7,0,8,6,8,

%U 4,7,4,4,2,2,0,3,2,2,0,1,6,5,5,4,3,0,3,4,9,7,1,5,1,2,3,0,2,5,6,8

%N 10-adic integer x such that x^3 = 7.

%H Seiichi Manyama, <a href="/A225405/b225405.txt">Table of n, a(n) for n = 0..10000</a>

%F Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + 7 * (b(n-1)^3 - 7) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. - _Seiichi Manyama_, Aug 13 2019

%e       3^3 == 7 (mod 10).

%e      43^3 == 7 (mod 10^2).

%e     543^3 == 7 (mod 10^3).

%e    1543^3 == 7 (mod 10^4).

%e   51543^3 == 7 (mod 10^5).

%e   51543^3 == 7 (mod 10^6).

%o (PARI) n=0; for(i=1, 100, m=7; for(x=0, 9, if(((n+(x*10^(i-1)))^3)%(10^i)==m, n=n+(x*10^(i-1)); print1(x", "); break)))

%o (PARI) N=100; Vecrev(digits(lift(chinese(Mod((7+O(2^N))^(1/3), 2^N), Mod((7+O(5^N))^(1/3), 5^N)))), N) \\ _Seiichi Manyama_, Aug 05 2019

%o (Ruby)

%o def A225405(n)

%o   ary = [3]

%o   a = 3

%o   n.times{|i|

%o     b = (a + 7 * (a ** 3 - 7)) % (10 ** (i + 2))

%o     ary << (b - a) / (10 ** (i + 1))

%o     a = b

%o   }

%o   ary

%o end

%o p A225405(100) # _Seiichi Manyama_, Aug 13 2019

%Y Cf. A225408, A309600.

%K nonn,base

%O 0,1

%A _Aswini Vaidyanathan_, May 07 2013