Extend many classic problems to bases 2 <= b <= 36

[sweety439]

1. Lychrel number (function "N + reverse of N" until reach a palindrome, e.g. 78 + 87 = 165, 165 + 561 = 726, 726 + 627 = 1353, 1353 + 3531 = 4884 and 4884 is palindrome)

2. Kaprekar's routine (for given number of digits, leading zeroes retained, e.g. if for 4 digit numbers, we reach a number 734, then we calculate 7430 - 0347 instead of 743 - 347)

3. Narcissistic number (also related project: Happy number, and we can extend happy number to other powers (not only 2nd powers))

4. Factorion

5. Dudeney number (we can extend to other powers (not only 3rd powers), also we can find "Dudeney sequence" with calculating (digit sum of N)^n)

6. Sum-product number

7. Keith number

8. Automorphic number (which is easier to find, this is equivalent to solve the equation x^2 = x in the ring of b-adic number) (we can also extend to Trimorphic numbers or further, by solve the equation x^3 = x and so on)

9. Harshad number and Zuckerman number

10. Polydivisible number

11. Friedman number (and its special case: Vampire number)

12. Multiplicative persistence problem

13. Smith number

14. Rhonda number

15. Self number (which in odd bases are less interesting, since such numbers are exactly the odd numbers)

16. Primeval number

17. Cyclic number and Parasitic number and Transposable integer (which can be calculate use the periodic part of base b expansion of 1/n)

18. Digit-reassembly number

19. Equidigital number and Extravagant number and Frugal number

20. Self-descriptive number (which has exactly one solution in all bases b >= 7)

and of course, the 13 base-dependent types of primes: https://mersenneforum.org/showpost.p...21&postcount=7, also two other base-dependent types of primes not shown in that page: Full reptend prime and Unique prime (which can be calculate use the periodic part of base b expansion of 1/p with prime p), also another four base-dependent types of primes not shown in that page: Undulating Palindromic Primes, Palindromic Wing Primes, Plateau and Depression Primes, Palindromic Merlon Primes, also the home prime problem

[mart_r]

Where's my number?