Here is a small python script which will serve your purpose.
# required import
import arcpy
# inputs
# feature class path
fc = r'C:\GISData\File Geodatabase.gdb\feature_class'
# interval
interval = 3
# --------------------- script ------------------------- #
selected_oid = []
ready_to_add = False
interval = abs(interval)
fc = arcpy.MakeFeatureLayer_management(fc, r'in_memory\fc_name')
with arcpy.da.SearchCursor(fc, 'OID@') as cur:
for i, row in enumerate(cur):
if i % interval == 0:
ready_to_add = not ready_to_add
if ready_to_add:
selected_oid.append(unicode(row[0]))
# where clause to select by attribute value
where = 'OBJECTID in ({})'.format(', '.join(selected_oid))
# selected features as required
selected_fc = arcpy.SelectLayerByAttribute_management(fc, "NEW_SELECTION", where)
Hope, this will help :)