A360424 Array read by rows: row n consists of the numbers k such that k^2 + (sum of n-th powers of the digits of k^2) is a square.

0, 0, 6, 0, 0, 89, 137, 6985, 0, 3072, 0, 68, 8346, 213202, 470102, 540674, 1014879, 0, 106329, 0, 37941, 1582656, 9244855, 45046529, 0, 1239, 5496, 14247, 490065

Offset: 1

Author

Robert Israel, Feb 06 2023

Keywords

• nonn
• tabf
• base
• more

Comments

T(n,1) = 0.

T(n,k) <= x where 9^n*(1+log_10(x^2)) = 2*x+1.

Examples

			Array begins:
  0
  0, 6
  0
  0, 89, 137, 6985
  0, 3072
  0, 68, 8346, 213202, 470102, 540674, 1014879
  0, 106329
  0, 37941, 1582656, 9244855, 45046529.
T(4,3) = 137 is a term because 137^2 = 18769 and 18769 + 1^4 + 8^4 + 7^4 + 6^4 + 9^4 = 182^2.
		

Crossrefs

Cf. A360422.

Programs

Maple

f:= proc(d) local k, kmax;
  kmax:= fsolve(k^2 + 9^d*(1+log[10](k^2))=(k+1)^2, k=0..infinity);
  select(k -> issqr(k^2 + add(t^d, t=convert(k^2,base,10))), [$0..floor(kmax)])
end proc:
seq(f(d), d=0..7);