A394718 - OEIS

%I #30 May 14 2026 21:38:13

%S 1,9,3025,1903664161,9903365616948251868225,

%T 22309173926869425179456178309988068048151564650625,

%U 347344242690551218689875522294777681772995698601451664233760078879673569943084142016961541085081108860391681

%N a(n) such that the n-th partial nested radical sqrt(a(1) + sqrt(a(2) + ... + sqrt(a(n)))) = n.

%C Every term in the sequence is a perfect square.

%C The number of digits in a(n) approximately doubles with each successive term.

%F a(n) = A083869(n)^2.

%e n = 1: sqrt(a(1)) = 1, so a(1) = 1;

%e n = 2: sqrt(a(1) + sqrt(a(2))) = 2, so a(2) = 9;

%e n = 3: sqrt(a(1) + sqrt(a(2) + sqrt(a(3)))) = 3, so a(3) = 3025;

%e n = 4: sqrt(a(1) + sqrt(a(2) + sqrt(a(3) + sqrt(a(4))))) = 4, so a(4) = 1903664161;

%e ...

%o (Python)

%o num_terms = 6 # Number of terms to be generated

%o a = [1]

%o for n in range(2, num_terms + 1):

%o     R = n

%o     for k in range(1, n):

%o         R = R**2 - a[k-1]

%o     a_n = R**2

%o     a.append(a_n)

%o print(a)

%Y Cf. A083869.

%K nonn,easy

%O 1,2

%A _S. S. Krishna Chaitanya Bulusu_, Apr 27 2026