A271226 - OEIS

%I #6 Apr 09 2016 13:01:59

%S 2,2,3,1,43,201,67,1289,2278,14662,53782,171798,57266,312537,104179,

%T 7353209,14081926,94917254,148495259,338541478,2498895558,832965186,

%U 277655062,45869694854,90480235883,230874654662

%N a(n) = (A271222(n)^2 + 2)/3^n, n >= 0.

%C a(n) is an integer because b(n) = A271222(n) satisfies b(n)^2 + 2 == 0 (mod 3^n), n >= 0.

%C See A268924 for details, links and references.

%F a(n) = (b(n)^2 + 2)/3^n, n >= 0, with b(n) = A271222(n).

%e a(0) = (0^2 + 2)/1 = 2.

%e a(4) = (59^2 + 2)/3^4 = 43.

%o (PARI) b(n) = if (n, 3^n - truncate(sqrt(-2+O(3^(n)))), 0);

%o a(n) = (b(n)^2 + 2)/3^n; \\ _Michel Marcus_, Apr 09 2016

%Y Cf. A268924, A271222, A271224, A271225 (companion sequence).

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Apr 05 2016