A225442 10-adic integer x such that x^7 = -1/3.

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

Offset: 0

Author

Aswini Vaidyanathan, May 11 2013

Keywords

• nonn
• base

Examples

			       7^7 == 3      (mod 10).
      37^7 == 33     (mod 10^2).
     437^7 == 333    (mod 10^3).
    7437^7 == 3333   (mod 10^4).
   57437^7 == 33333  (mod 10^5).
  257437^7 == 333333 (mod 10^6).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Programs

PARI

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

PARI

N=100; Vecrev(digits(lift(chinese(Mod((-1/3+O(2^N))^(1/7), 2^N), Mod((-1/3+O(5^N))^(1/7), 5^N)))), N) \\ Seiichi Manyama, Aug 06 2019