A372147 Numbers k for which k and k^2 are digitally balanced numbers in base 3 (A049354).
500, 544, 550, 552, 588, 622, 307172, 307402, 307888, 308920, 309480, 309522, 309604, 310348, 310422, 310658, 310754, 310964, 310974, 310980, 311206, 311214, 311342, 311466, 311582, 311788, 311790, 312050, 312070, 312100, 313022, 313050, 313336, 313502, 313512
Offset: 1
Examples
500 = 200112_3 and 500^2 = 250000 =110200221021_3, so 500 is a term. 544 = 202011_3 and 544^2 = 295936 =120000221121_3, so 544 is a term.
Programs
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Magma
bal:=func
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Mathematica
balQ[n_, b_] := MinMax@ Differences@ DigitCount[n, b] == {0, 0}; Select[Range[320000], balQ[#, 3] && balQ[#^2, 3] &] (* Amiram Eldar, Jun 03 2024 *)