Narcissistic number

The narcissistic numbers are a subset of natural numbers, the generation by certain computational rules of its digits yourself. They play in pure mathematics, however, no particular role ( ie usually the decimal system ) because they depend strongly on the used number system and thus bring no real scientific value.

• 2.1 Example

• 3.1 Example

• 4.1 Example

• 5.1 Examples

Pluperfect digital invariants (also Armstrong numbers)

The PPDI are narcissistic numbers whose sum of its digits, each raised to the power of the number of digits in the number, again yields the number itself ( sequence A005188 in OEIS ). A number, is a PPDI, if applies.

Example

An example of such a number to the power of n = 5 54748:

There are a total of exactly 88 narcissistic numbers in the decimal system, 115,132,219,018,763,992,565,095,597,973,971,522,401 with 39 points, the largest.

Narcissistic numbers with increasing potency

Are numbers whose sum of its digits raised to its place in the number, the number makes itself. So a number abc =. The number of points is not limited to 3. There are, for example, 9 - and more narcissistic digit numbers.

Example

The following numbers are in this sense, narcissistic: 89, 135, 175, 518, 598, 1306, 1676, 2427, 2646798, ... ( sequence A032799 in OEIS )

Narcissistic numbers with a constant base

Are numbers, where the base is constant and the exponent corresponding to the digits of the number.

Example

Wild narcissistic numbers

Are numbers where the manner in which they themselves produce from their digits is not uniform.

Example

Interesting numbers

Are more free than the wild narcissistic numbers in their generation:

Examples