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An odious number is a nonnegative number that has an odd number of 1s in its binary expansion. The first few odious numbers are therefore 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, ...

A fraction containing each of the digits 1 through 9 is called a pandigital fraction. The following table gives the number of pandigital fractions which represent simple unit ...

An n-persistent number is a positive integer k which contains the digits 0, 1, ..., 9 (i.e., is a pandigital number), and for which 2k, ..., nk also share this property. No ...

The previous prime function PP(n) gives the largest prime less than n. The function can be given explicitly as PP(n)=p_(pi(n-1)), where p_i is the ith prime and pi(n) is the ...

The sequence obtained from reversing the digits of a number n and adding the result to the original number. For n=1, 2, ..., this gives 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, ...

The nth Smarandache-Wellin number is formed from the consecutive number sequence obtained by concatenating of the digits of the first n primes. The first few are 2, 23, 235, ...

The sequence produced by sorting the digits of a number and adding them to the previous number. The values starting with n=1, 2, ... are 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, ...

A tetradic (or four-way) number is a number that remains unchanged when flipped back to front, mirrored up-down, or flipped up-down. Since the only numbers that remain ...

A number n such that the last digits of n^3 are the same as n. 49 is trimorphic since 49^3=117649 (Wells 1986, p. 124). The first few are 1, 4, 5, 6, 9, 24, 25, 49, 51, 75, ...

An unhappy number is a number that is not happy, i.e., a number n such that iterating this sum-of-squared-digits map starting with n never reaches the number 1. The first few ...