A260489 a(n) = 3n - A260488(n).

0, 2, 4, 5, 5, 7, 5, 7, 8, 8, 5, 7, 8, 8, 10, 8, 10, 8, 5, 7, 8, 8, 10, 8, 10, 11, 11, 8, 10, 11, 11, 8, 10, 8, 5, 7, 8, 8, 10, 8, 10, 11, 11, 8, 10, 11, 11, 13, 11, 13, 11, 8, 10, 11, 11, 13, 11, 13, 11, 8, 10, 11, 11, 8, 10, 8, 5, 7, 8, 8, 10

Offset: 0

Author

Franklin T. Adams-Watters, Jul 27 2015

Keywords

• nonn

Comments

The sequence is nonnegative for at least the first 10000 terms, so the nonn keyword was used. That it is always nonnegative is a conjecture. That it is unbounded is also a conjecture.

The sequence is nonnegative for essentially the reason given in A225838 for its terms exceeding the terms of its complement. Here, the customers are labeled with numbers, m, that are powers of 2 and they each deposit 2 coins at each epoch (6k+1)*m and withdraw them separately at epoch (6k+3)*m and (6k+5)*m. The terms here are the number of coins in the vault after the n-th deposit. Simple accountancy says the sum of nonnegative bank balances is nonnegative. - Peter Munn, Nov 15 2023

Crossrefs

Cf. A008585, A225838, A260488.