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A339134 Indices in A338884 where records occur.

%I A339134 #6 Nov 26 2020 23:06:52
%S A339134 1,4,12,66,346,5876,95078,9411222,1894078221
%N A339134 Indices in A338884 where records occur.
%C A339134 It seems that A338884(a(n)) = n and 3*sqrt(log(a(n)))/n ~ O(1).
%o A339134 (Python)
%o A339134 from sympy import isprime
%o A339134 def search(n):
%o A339134     k = 1
%o A339134     while 1:
%o A339134         i = k*n + 1
%o A339134         while i < k*n + k:
%o A339134             if isprime(i) == 1: return i
%o A339134             i += 2
%o A339134         k = 2*k
%o A339134 a_rec = 0
%o A339134 n = 1
%o A339134 while 1:
%o A339134     m = search(n)
%o A339134     a = m.bit_length() - n.bit_length()
%o A339134     if a > a_rec:
%o A339134         print(n)
%o A339134         a_rec = a
%o A339134     n += 1
%Y A339134 Cf. A000040, A070939, A208241, A338884.
%K A339134 nonn,base,more
%O A339134 1,2
%A A339134 _Ya-Ping Lu_, Nov 24 2020