I do not know of any arcpy functions to do this...You will need to use the method that James provided using the modulus. You could do something like this:
import arcpy
fc = r'G:\Data\Geodatabase\Cedar_County.gdb\JURISDICTION\CORP_LIM'
oid = arcpy.Describe(fc).OIDFieldName
even = []
odd = []
rows = arcpy.SearchCursor(fc)
for row in rows:
fid = row.getValue(oid)
if fid %2 == 0:
even.append(fid)
else:
odd.append(fid)
del row, rows
field = arcpy.AddFieldDelimiters(fc, oid)
even_sql = ' OR '.join('%s = %s' %(field,i) for i in even)
odd_sql = ' OR '.join('%s = %s' %(field,i) for i in odd)
# Make Feature layers
lyr = arcpy.MakeFeatureLayer_management(fc, 'Temp_layer')
# Select Even
arcpy.SelectLayerByAttribute_management(lyr, 'NEW_SELECTION', even_sql)
# Select odd
arcpy.SelectLayerByAttribute_management(lyr, 'NEW_SELECTION', odd_sql)
OR, if you have a lot of features it may not be practical to build a very long query. You may want to temporarily add a field to tell whether the fid is even or odd (these fid's are subject to change with shapefiles so be careful) and select using that new field:
import arcpy
fc = r'G:\Data\Geodatabase\Cedar_County.gdb\JURISDICTION\CORP_LIM'
oid = arcpy.Describe(fc).OIDFieldName
#Add Field to tell if even/odd
arcpy.AddField_management(fc, 'Type', 'TEXT',4)
rows = arcpy.UpdateCursor(fc)
for row in rows:
fid = row.getValue(oid)
if fid %2 == 0:
row.Type = 'Even'
else:
row.Type = 'Odd'
rows.updateRow(row)
del row, rows
typeField = arcpy.AddFieldDelimiters(fc, 'Type')
even_sql = "%s = 'Even'" %typeField
odd_sql = "%s = 'Odd'" %typeField
# Make Feature layers
lyr = arcpy.MakeFeatureLayer_management(fc, 'Temp_layer')
# Select Even
arcpy.SelectLayerByAttribute_management(lyr, 'NEW_SELECTION', even_sql)
# Select odd
arcpy.SelectLayerByAttribute_management(lyr, 'NEW_SELECTION', odd_sql)