A255310 Positive integers not the sum of iterated binary logs.

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

Links

Table of n, a(n) for n=1..33.

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

Cf. A232779, A255309.

Sequence in context: A319140 A336902 A135476 * A051217 A275522 A110975

Adjacent sequences: A255307 A255308 A255309 * A255311 A255312 A255313

Keyword

nonn,easy

Author

Paul Boddington, Feb 20 2015

Status

approved