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A376758 The terms of A376201 consist of runs of successive numbers that increase by 1 at each step: a(n) is one-half of length of the n-th such run.

%I A376758 #15 Oct 15 2024 12:19:22
%S A376758 2,1,1,1,2,1,3,3,6,3,1,2,1,4,1,7,2,13,7,2,5,5,13,7,1,3,3,6,7,32,4,7,
%T A376758 10,16,8,4,4,1
%N A376758 The terms of A376201 consist of runs of successive numbers that increase by 1 at each step: a(n) is one-half of length of the n-th such run.
%C A376758 [At present it is only a conjecture that the runs have even length, but the proof should not be difficult.]
%e A376758 A376201 begins 1, 2, 3, 4, 11, 12, 27, 28, 59, 60, 123, 124, 125, 126, 255, ...
%e A376758 The runs have lengths 4,2,2,4,... so the present sequence begins 2,1,1,2,...
%o A376758 (Python)
%o A376758 from itertools import count, islice
%o A376758 from sympy import isprime, nextprime
%o A376758 def A376758_gen(): # generator of terms
%o A376758     c, a, p, q = 2, 2, 3, 4
%o A376758     for n in count(3):
%o A376758         b = min(p,q) if isprime(a) else (p if a == (p<<1) else q)
%o A376758         if b == n:
%o A376758             if b == a+1:
%o A376758                 c += 1
%o A376758             else:
%o A376758                 yield c>>1
%o A376758                 c = 1
%o A376758         if b == p:
%o A376758             p = nextprime(p)
%o A376758         else:
%o A376758             q += isprime(q+1)+1
%o A376758         a = b
%o A376758 A376758_list = list(islice(A376758_gen(),10)) # _Chai Wah Wu_, Oct 14 2024
%Y A376758 Cf. A376198, A376201.
%K A376758 nonn,more
%O A376758 1,1
%A A376758 _N. J. A. Sloane_, Oct 07 2024
%E A376758 a(33)-a(35) from _Michael S. Branicky_, Oct 08 2024
%E A376758 a(36)-a(38) from _Michael S. Branicky_, Oct 15 2024