A255310 - OEIS

%I #12 Mar 03 2015 20:43:50

%S 2,5,6,11,20,21,22,39,72,137,266,267,524,1037,2062,4111,8208,16401,

%T 32786,65555,65556,65557,65558,131095,262168,524313,1048602,2097179,

%U 4194332,8388637,16777246,33554463,67108896

%N Positive integers not the sum of iterated binary logs.

%e Clearly A232779 is increasing, and A232779(n) equals 1 + A232779(n - 1) unless n is a power of 2. Therefore this sequence consists of all numbers strictly between A232779(2^r - 1) and A232779(2^r) for some r. For example, A232779(15) = 15 + 3 + 1 = 19, whereas A232779(16) = 16 + 4 + 2 + 1 = 23, so this sequence includes the terms 20, 21, 22.

%e The sequence can also be obtained using the sequence b(n) = A255309(n).

%e Suppose t >= 2 is a power of 2. Let s be the sum of b(r) for r from 1 to t - 1.

%e Then the numbers t + s (inclusive) to t + s + b(t) (exclusive) are in this sequence, and all terms can be obtained in this way.

%e For example, if t = 16, then s = b(1) + b(2) + ... + b(15) = 4, and b(16) = 3, so the bounds are 16 + 4 = 20 and 16 + 4 + 3 = 23, producing the terms 20, 21, 22.

%Y Cf. A232779, A255309.

%K nonn,easy

%O 1,1

%A _Paul Boddington_, Feb 20 2015