Sloane's gap is a sparsely populated band separating two clouds in a scatter diagram of the occurrence counts of integers in a
historical version of the On-Line Encyclopedia of Integer Sequences (OEIS). Let 
count the appearances of 
in the stored initial terms of integer
sequences. The reported plot shows 
horizontally and 
vertically for 
, 2, ..., 10000, where 
is the natural logarithm
(Gauvrit et al. 2013).
For example, the February 2009 counts cited in the study were 
, 
, and 
. The boundary separating the clouds was chosen empirically,
and the gap was not completely empty. Among the integers
from 301 to 10000, prime numbers and square
numbers were concentrated in the upper cloud.
Gauvrit et al. (2013) discussed Kolmogorov complexity in connection with the overall shape of the distribution and proposed shared mathematical preferences as an explanation of the gap. This is an explanatory hypothesis about the curated data. The counts depend on the database version and the stored prefixes, and do not define an intrinsic classification of integers by interest.
The illustration uses the OEIS snapshot of October 24, 2026 at 07:00:17 UTC and counts the stored terms of 398,559 retained integer sequences out of 400,652 records (OEIS Foundation Inc. 2026). The sample excludes 1,962 records marked dead and 131 further records identified in individual screening as erroneous, duplicated, nonsensical, obsolete, or unresolved. Of the retained integer sequences, 388,806 contain at least one integer from 1 through 10000. Prime numbers are blue, square numbers are orange, and other integers are gray. The vertical scale is logarithmic.
