A376483 Perfect squares k for which sqrt(k) = (Sum of digits of k) - 2.

4, 25, 64, 196, 289

Offset

1,1

Comments

The corresponding square roots are 2, 5, 8, 14, 17.

These squares are connected via the Pythagorean quadruple 2^2 + 5^2 + 8^2 + 14^2 = 17^2.

These are the only such numbers. No additional solutions exist for k ≤ 34^2 = 1156, and sqrt(k) outpaces the sum of digits of k beyond this point.

Links

Table of n, a(n) for n=1..5.

Example

k=25 is a term since sqrt(25) = 5 and sum of digits of 25 is 7 and 5 = 7 - 2.

Prog

(SageMath)
def find_numbers(limit=1156):
    valid_numbers = []
    for s in range(1, int(sqrt(limit)) + 1):
        N = s**2
        digit_sum = sum(int(d) for d in str(N))
        if sqrt(N) == digit_sum - 2:
            valid_numbers.append(N)
    return valid_numbers

Crossrefs

Cf. A000290 (squares), A002620 (squares sum of four squares).

Sequence in context: A065733 A368245 A212893 * A302324 A303017 A281339

Adjacent sequences: A376480 A376481 A376482 * A376484 A376485 A376486

Keyword

nonn,fini,full,base

Author

Lucas Sacramento, Sep 24 2024

Status

approved