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Missing-digit sums are integer numbers that are equal to the sum of numbers created by deleting one or more digits at a time from the original number. For example, the OEIS lists these two integers as missing-digit sums in base ten: :1,729,404 = 729404 (missing 1) + 129404 (missing 7) + 179404 (missing 2) + 172404 + 172904 + 172944 + 172940 :1,800,000 = 800000 (missing 1) + 100000 (missing 8) + 180000 (missing first 0) + 180000 + 180000 + 180000 + 180000 Missing-digit sums are therefore a subset of narcissistic numbers, when these are defined as numbers that are equal to some manipulation of their own digits (for example, 153 and 132 are narcissistic numbers in base ten because 153 = 13 + 53 + 33 and 132 = 13 + 32 + 12 + 31 + 23 + 21). ==Dropping two and more digits== When one digit is dropped from a ''d''-digit integer, there are ''d'' integers in the sum and each is ''d''-1 digits long. In general, when ''n'' digits are dropped from a ''d''-digit integer, the number of integers in the sum is equal to ''d''! / (''n''!(''d'' - ''n'')!), or the combination of ''n'' digits taken 2, 3, 4... at a time. For example, when ''d'' = 20 and ''n'' = 3, there are 20! / (3!(20 - 3)!) = 1,140 integers in the sum. In base ten, the integers 183477122641, 1523163197662495253514 and 47989422298181591480943 are equal to their missing-digit sums when dropping two, three and four digits, respectively. Here is the delete-2 sum, containing 12! / (2!(12 - 2)!) = 66 integers: :183477122641 = 3477122641 (missing 1 and 8) + 8477122641 (missing 1 and 3) + 8377122641 (missing 1 and 4) + 8347122641 (missing 1 and first 7) + 8347122641 (missing 1 and second 7) + 8347722641 (missing 1 and second 1) + 8347712641 + 8347712641 + 8347712241 + 8347712261 + 8347712264 + 1477122641 + 1377122641 + 1347122641 + 1347122641 + 1347722641 + 1347712641 + 1347712641 + 1347712241 + 1347712261 + 1347712264 + 1877122641 + 1847122641 + 1847122641 + 1847722641 + 1847712641 + 1847712641 + 1847712241 + 1847712261 + 1847712264 + 1837122641 + 1837122641 + 1837722641 + 1837712641 + 1837712641 + 1837712241 + 1837712261 + 1837712264 + 1834122641 + 1834722641 + 1834712641 + 1834712641 + 1834712241 + 1834712261 + 1834712264 + 1834722641 + 1834712641 + 1834712641 + 1834712241 + 1834712261 + 1834712264 + 1834772641 + 1834772641 + 1834772241 + 1834772261 + 1834772264 + 1834771641 + 1834771241 + 1834771261 + 1834771264 + 1834771241 + 1834771261 + 1834771264 + 1834771221 + 1834771224 + 1834771226 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Missing-digit sum」の詳細全文を読む スポンサード リンク
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