login
A255310
Positive integers not the sum of iterated binary logs.
0
2, 5, 6, 11, 20, 21, 22, 39, 72, 137, 266, 267, 524, 1037, 2062, 4111, 8208, 16401, 32786, 65555, 65556, 65557, 65558, 131095, 262168, 524313, 1048602, 2097179, 4194332, 8388637, 16777246, 33554463, 67108896
OFFSET
1,1
EXAMPLE
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.
The sequence can also be obtained using the sequence b(n) = A255309(n).
Suppose t >= 2 is a power of 2. Let s be the sum of b(r) for r from 1 to t - 1.
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.
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.
CROSSREFS
Sequence in context: A336902 A373243 A135476 * A051217 A275522 A110975
KEYWORD
nonn,easy
AUTHOR
Paul Boddington, Feb 20 2015
STATUS
approved