A394718 a(n) such that the n-th partial nested radical sqrt(a(1) + sqrt(a(2) + ... + sqrt(a(n)))) = n.

1, 9, 3025, 1903664161, 9903365616948251868225, 22309173926869425179456178309988068048151564650625, 347344242690551218689875522294777681772995698601451664233760078879673569943084142016961541085081108860391681

Offset

1,2

Comments

Every term in the sequence is a perfect square.

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

Links

Table of n, a(n) for n=1..7.

Formula

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

Example

n = 1: sqrt(a(1)) = 1, so a(1) = 1;
n = 2: sqrt(a(1) + sqrt(a(2))) = 2, so a(2) = 9;
n = 3: sqrt(a(1) + sqrt(a(2) + sqrt(a(3)))) = 3, so a(3) = 3025;
n = 4: sqrt(a(1) + sqrt(a(2) + sqrt(a(3) + sqrt(a(4))))) = 4, so a(4) = 1903664161;
...

Prog

(Python)
num_terms = 6 # Number of terms to be generated
a = [1]
for n in range(2, num_terms + 1):
    R = n
    for k in range(1, n):
        R = R**2 - a[k-1]
    a_n = R**2
    a.append(a_n)
print(a)

Crossrefs

Cf. A083869.

Sequence in context: A321282 A159775 A389385 * A281538 A335010 A203744

Adjacent sequences: A394715 A394716 A394717 * A394719 A394720 A394721

Keyword

nonn,easy

Author

S. S. Krishna Chaitanya Bulusu, Apr 27 2026

Status

approved