Self number / Devlali Number / Swayambhu' Number was discovered by Indian mathematician Dattathreya Ramchandra Kaprekar who was born in Dhanu (Maharastra).
A self number is a number that cannot be written as the sum of any other integer n and the individual digits of n. It was discovered in 1949 by Kaprekar.
These are the self number
1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, 97, 108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 211, 222, 233, 244 - - -
Start with a number, say 23. The sum of its digits (2 + 3) are 5 which we add to 23 to obtain 28. Again add 2 and 8 to get 10 which we add to 28 to get 38. Continuing gives the sequence
23, 28, 38, 49, 62, 70, ...
These are all generated by 23. But is 23 generated by a smaller number? Yes, 16 generates 23. In fact the sequence we looked at really starts at 1
1, 2, 4, 8, 16, 23, 28, 38, 49, 62, 70, ...
Here is the recurrence formula to find the Self Number
where
(Sources :- Wikipedia / Mac Tutor Archive )
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Dr Rajesh Kumar Thakur
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