A360422 Numbers k such that k^2 + (sum of fourth powers of the digits of k^2) is a square.

0, 89, 137, 6985

Offset

1,2

Comments

Since A055013(k) < 9^4*(1+log_10(k)) and k^2 + 9^4*(1+log_10(k^2)) < (k+1)^2 for k > 32918, one need only search up to k = 32918.

Links

Table of n, a(n) for n=1..4.

Example

a(3) = 137 is a term because 137^2 = 18769 and 18769 + 1^4 + 8^4 + 7^4 + 6^4 + 9^4 = 182^2.

Maple

select(n -> issqr(n^2 + add(t^4, t = convert(n^2, base, 10))), [$0..32918]);

Prog

(Python)
from math import isqrt
def sq(n): return isqrt(n)**2 == n
def ok(n): return sq(n**2 + sum(int(d)**4 for d in str(n**2)))
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Feb 12 2023

Crossrefs

Cf. A055013, A360424.

Sequence in context: A132258 A257860 A256242 * A109560 A260557 A141938

Adjacent sequences: A360419 A360420 A360421 * A360423 A360424 A360425

Keyword

nonn,bref,fini,full,base

Author

Robert Israel and Will Gosnell, Feb 06 2023

Status

approved