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A376483
Perfect squares k for which sqrt(k) = (Sum of digits of k) - 2.
0
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.
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
KEYWORD
nonn,fini,full,base
AUTHOR
Lucas Sacramento, Sep 24 2024
STATUS
approved