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
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
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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);
Comments