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a[n_] := Plus @@ Mod[NestWhileList[(# - Mod[#, 4])/-4 &, n, # != 0 &], 4]; Array[a, 100, 0] (* Amiram Eldar, Mar 22 2021 *)
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D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1969, Vol. 2, p. 172, . (Also exercise 16, p. 177, answer, p. 494.)
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