cp's OEIS Frontend

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

%I A360422 #11 Feb 13 2023 02:28:32
%S A360422 0,89,137,6985
%N A360422 Numbers k such that k^2 + (sum of fourth powers of the digits of k^2) is a square.
%C A360422 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.
%e A360422 a(3) = 137 is a term because 137^2 = 18769 and 18769 + 1^4 + 8^4 + 7^4 + 6^4 + 9^4 = 182^2.
%p A360422 select(n -> issqr(n^2 + add(t^4, t = convert(n^2,base,10))), [$0..32918]);
%o A360422 (Python)
%o A360422 from math import isqrt
%o A360422 def sq(n): return isqrt(n)**2 == n
%o A360422 def ok(n): return sq(n**2 + sum(int(d)**4 for d in str(n**2)))
%o A360422 print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Feb 12 2023
%Y A360422 Cf. A055013, A360424.
%K A360422 nonn,bref,fini,full,base
%O A360422 1,2
%A A360422 _Robert Israel_ and _Will Gosnell_, Feb 06 2023