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%I #32 Nov 28 2019 22:44:26
%S 2,3,4,4,2,5,2,2,2,8,2,2,2,5,3,2,2,3,2,2,3,4,2,3,3,2,2,3,2,3,2,2,2,2,
%T 3,2,2,2,2,4,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,3,3,2,2,6,2,2,26,2,2,3,2,
%U 2,2,2,2,2,2,5,2,3,2,2
%N a(n) = ceiling(A002386(n+1)/A002386(n)).
%C Obviously, for all n, a(n) is greater than one. According to the definition of a(n) for all n, A002386(n+1) < a(n)*A002386(n). So if n is less than 79 and not equal to 64, then A002386(n+1) < 8*A002386(n). [Updated _John W. Nicholson_, Nov 28 2019]
%C Also for all n < 79, A002386(n+1) < 26*A002386(n). [Updated _John W. Nicholson_, Nov 28 2019]
%C The strictly increasing terms of the sequence: 2, 3, 4, 5, 8, 26, ?, ... .
%C Record values are {2, 3, 4, 5, 8, 26} = {a(1), a(2), a(3), a(6), a(10), a(64)}.
%C A very difficult question: "What is the next term of the above sequence?" namely "What is the next term of the sequence which is greater than a(64) = 26 ?". I don't think that in this century anyone can find the answer.
%F a(n) = ceiling(A002386(n+1)/A002386(n)) = floor(A002386(n+1)/A002386(n))+1.
%e a(10) = ceiling(A002386(11)/A002386(10)) = ceiling(9551/1327) = 8.
%Y Cf. A000040, A002386.
%K nonn,more,hard
%O 1,1
%A _Farideh Firoozbakht_, Oct 08 2014
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