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A366475 a(n) = (A364054(n) - A366470(n))/prime(n-1).

%I A366475 #28 Oct 28 2023 00:25:07
%S A366475 1,2,2,0,1,0,1,2,2,1,2,0,1,0,1,0,1,0,1,0,1,2,0,1,0,1,2,3,0,2,0,1,0,1,
%T A366475 0,2,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
%U A366475 0,1,0,1,0,1,0,1,0,1,2,0,1,2,2,1,2,1,2,0,1,2,0,2,0
%N A366475 a(n) = (A364054(n) - A366470(n))/prime(n-1).
%C A366475 a(29) = 3. When, if ever, does 4 appear?
%C A366475 Answer: a(28025) = 4. - _Michael De Vlieger_, Oct 26 2023
%H A366475 Michael De Vlieger, <a href="/A366475/b366475.txt">Table of n, a(n) for n = 2..65536</a>
%H A366475 Michael De Vlieger, <a href="/A366475/a366475.png">2048 X 2048 raster showing a(n)</a>, n = 1..4194304 in rows of 2048 terms, left to right, then continued below for 2048 rows total. Color indicates terms as follows: black = 0, blue = 1, green = 2, gold = 3, red = 4.
%e A366475    n p(n-1)  x   y  a(n)  [x = A364054(n), y = A366470(n)]
%e A366475    1   (1)   1   -   -    [a(n) = (x-y)/p(n-1)]
%e A366475    2    2    3   1   1
%e A366475    3    3    6   0   2
%e A366475    4    5   11   1   2
%e A366475    5    7    4   4   0
%e A366475    6   11   15   4   1
%e A366475    7   13    2   2   0
%e A366475 ...
%t A366475 nn = 2^20;
%t A366475   c[_] := False; m[_] := 0; a[1] = j = 1; c[0] = c[1] = True;
%t A366475   Monitor[Do[p = Prime[n - 1]; r = Mod[j, p];
%t A366475     While[Set[k, p m[p] + r ]; c[k], m[p]++];
%t A366475     Set[{a[n], b[n], c[k], j}, {k, m[p], True, k}], {n, 2, nn}], n];
%t A366475 Array[b, nn-1, 2] (* _Michael De Vlieger_, Oct 26 2023 *)
%o A366475 (Python)
%o A366475 from itertools import count, islice
%o A366475 from sympy import nextprime
%o A366475 def A366475_gen(): # generator of terms
%o A366475     a, aset, p = 1, {0,1}, 1
%o A366475     while True:
%o A366475         p = nextprime(p)
%o A366475         b = a%p
%o A366475         for i in count(0):
%o A366475             if b not in aset:
%o A366475                 aset.add(b)
%o A366475                 a = b
%o A366475                 break
%o A366475             b += p
%o A366475         yield i
%o A366475 A366475_list = list(islice(A366475_gen(),30)) # _Chai Wah Wu_, Oct 27 2023
%Y A366475 Cf. A364054, A366470, A366477 (records).
%K A366475 nonn
%O A366475 2,2
%A A366475 _N. J. A. Sloane_, Oct 26 2023