A244445 a(n) = ceiling(A002386(n+1)/A002386(n)).

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, 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, 2, 2, 2, 2, 2, 2, 5, 2, 3, 2, 2

Offset: 1

Author

Farideh Firoozbakht, Oct 08 2014

Keywords

• nonn
• more
• hard

Comments

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]

Also for all n < 79, A002386(n+1) < 26*A002386(n). [Updated John W. Nicholson, Nov 28 2019]

The strictly increasing terms of the sequence: 2, 3, 4, 5, 8, 26, ?, ... .

Record values are {2, 3, 4, 5, 8, 26} = {a(1), a(2), a(3), a(6), a(10), a(64)}.

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.

Examples

			a(10) = ceiling(A002386(11)/A002386(10)) = ceiling(9551/1327) = 8.
		

Crossrefs

Cf. A000040, A002386.

Formula

a(n) = ceiling(A002386(n+1)/A002386(n)) = floor(A002386(n+1)/A002386(n))+1.