A246819 Max_{2<=k<=n} floor(A242719(k)/prime(k)) - prime(n).

0, 0, 0, 4, 2, 4, 2, 13, 7, 13, 7, 4, 2, 0, 17, 11, 9, 6, 2, 24, 21, 17, 11, 12, 8, 6, 2, 18, 29, 15, 11, 5, 3, 16, 14, 8, 18, 14, 8, 22, 20, 10, 30, 29, 27, 15, 3, 6, 8, 4, 0, 30, 20, 14, 60, 54, 52, 46, 42, 40, 30, 16, 12, 10, 41, 27, 21, 11, 20, 16, 10, 6

Offset: 2

Author

Vladimir Shevelev, Sep 04 2014

Keywords

• nonn

Comments

Conjecture: a(n) = o(prime(n)), as n goes to infinity.

If the conjecture is true, then A242719(n) ~ prime(n)^2. Indeed, A242719(n) >= prime(n)^2 + 1; on the other hand, by the conjecture, we have A242719(n)/prime(n) <= a(n) + 1 + prime(n) = prime(n)*(1+o(1)).

Links

• Peter J. C. Moses, Table of n, a(n) for n = 2..2001

Crossrefs

Cf. A242719, A242720, A246748, A246821.

Extensions

More terms from Peter J. C. Moses, Sep 04 2014