A225458 - OEIS

%I #17 Aug 14 2019 08:32:35

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

%T 3,2,4,9,5,0,4,9,4,0,0,9,4,7,4,6,6,3,3,6,5,1,7,2,1,9,9,0,9,0,5,1,4,9,

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

%N 10-adic integer x such that x^9 = 9.

%H Seiichi Manyama, <a href="/A225458/b225458.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) = 9, b(n) = b(n-1) + b(n-1)^9 - 9 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. - _Seiichi Manyama_, Aug 14 2019

%e        9^9 == 9 (mod 10).

%e       89^9 == 9 (mod 10^2).

%e      289^9 == 9 (mod 10^3).

%e     1289^9 == 9 (mod 10^4).

%e    21289^9 == 9 (mod 10^5).

%e   921289^9 == 9 (mod 10^6).

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

%o (PARI) N=100; Vecrev(digits(lift(chinese(Mod((9+O(2^N))^(1/9), 2^N), Mod((9+O(5^N))^(1/9), 5^N)))), N) \\ _Seiichi Manyama_, Aug 06 2019

%o (Ruby)

%o def A225458(n)

%o   ary = [9]

%o   a = 9

%o   n.times{|i|

%o     b = (a + a ** 9 - 9) % (10 ** (i + 2))

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

%o     a = b

%o   }

%o   ary

%o end

%o p A225458(100) # _Seiichi Manyama_, Aug 14 2019

%Y Digits of the k-adic integer (k-1)^(1/(k-1)): A309698 (k=4), A309699 (k=6), A309700 (k=8), this sequence (k=10).

%K nonn,base

%O 0,1

%A _Aswini Vaidyanathan_, May 11 2013