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All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. For numbers with three identical digits and a fourth digit that is one higher or lower (such as 2111), it is essential to treat 3-digit numbers with a leading zero; for example: 2111 – 1112 = 0999; 9990 – 999 = 8991; 9981 – 1899 ...
A property of weird numbers is that if n is weird, and p is a prime greater than the sum of divisors σ(n), then pn is also weird. [4] This leads to the definition of primitive weird numbers: weird numbers that are not a multiple of other weird numbers (sequence A002975 in the OEIS). Among the 1765 weird numbers less than one million, there are ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers
The smallest base greater than binary such that no three-digit narcissistic number exists. 80: Octogesimal: Used as a sub-base in Supyire. 85: Ascii85 encoding. This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 ...
A solid serial number is one where every digit is the same, like 55555555. Only about one out of every 11 million notes is a solid, and they can be worth $500 or more. Some super-rare ones are ...
the k given prime numbers p i must be precisely the first k prime numbers (2, 3, 5, ...); if not, we could replace one of the given primes by a smaller prime, and thus obtain a smaller number than n with the same number of divisors (for instance 10 = 2 × 5 may be replaced with 6 = 2 × 3; both have four divisors);
The first number remaining in the list after 1 is 3, so every third number (beginning at 1) which remains in the list (not every multiple of 3) is eliminated. The first of these is 5: 1: 3: 7: 9: 13: 15: 19: 21: 25 The next surviving number is now 7, so every seventh remaining number is eliminated. The first of these is 19: 1: 3: 7: 9: 13: 15 ...