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A348446 a(n) = A307720(2*n-1) - A307220(2*n).

%I A348446 #28 Oct 26 2021 06:52:23
%S A348446 0,1,2,1,0,0,1,1,0,0,0,0,0,2,2,2,2,1,1,1,1,1,1,4,4,4,6,6,6,5,3,3,3,3,
%T A348446 3,5,5,5,5,5,5,4,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,
%U A348446 6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,5,1,1,1,1,1,1,1
%N A348446 a(n) = A307720(2*n-1) - A307220(2*n).
%C A348446 My guess is that this changes signs infinitely often, but is more likely to be positive than negative. Perhaps the behavior is akin to that of A066520, which shows the "great prime race" between primes congruent to 3 mod 4 and primes congruent to 1 mod 4.
%C A348446 See also the graphs in A307720 and A348248.
%H A348446 N. J. A. Sloane, <a href="/A348446/b348446.txt">Table of n, a(n) for n = 1..20000</a>
%H A348446 Rémy Sigrist, <a href="/A348446/a348446.png">Scatterplot of the first million terms</a>
%H A348446 Rémy Sigrist, <a href="/A348446/a348446_1.png">Scatterplot of the first five million terms</a>
%H A348446 N. J. A. Sloane, <a href="/A348446/a348446.txt">Table of n, a(n) for n = 1..500000</a>
%H A348446 Chai Wah Wu, <a href="/A348446/a348446_2.png">Scatterplot of the first 100 million terms</a>
%o A348446 (Python)
%o A348446 from itertools import islice
%o A348446 from collections import Counter
%o A348446 def A348446(): # generator of terms. Greedy algorithm
%o A348446     a = 1
%o A348446     c, b = Counter(), 1
%o A348446     while True:
%o A348446         k, kb = 1, b
%o A348446         while c[kb] >= kb:
%o A348446             k += 1
%o A348446             kb += b
%o A348446         c[kb] += 1
%o A348446         b = k
%o A348446         a2 = k
%o A348446         yield a-a2
%o A348446         k, kb = 1, b
%o A348446         while c[kb] >= kb:
%o A348446             k += 1
%o A348446             kb += b
%o A348446         c[kb] += 1
%o A348446         b = k
%o A348446         a = k
%o A348446 A348446_list = list(islice(A348446(),100)) # _Chai Wah Wu_, Oct 23 2021
%Y A348446 Cf. A066520, A307720, A307730, A348248.
%K A348446 sign
%O A348446 1,3
%A A348446 _N. J. A. Sloane_, Oct 22 2021