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nialpdromes
A number is a nialpdrome in a given base    (often 10 or 16) if its digits are in nonincreasing order in that base.

For example, 43210, 2222, 76652 and 9630 are all nialpdromes in base 10.

A nialpdrome in which the digits are strictly decreasing is called katadrome, while numbers whose digits are deincreasing and strictly decreasing are called plaindromes and metadromes.

The number    of nialpdromes of    digits in base    is equal to

which, for    simplifies to  . In general  , since we count also the 0 among the 1-digit nialpdromes.

The total number    of nialpdromes in base   with at most    digits is equal to

Probably the largest nialpdrome primes with index respectively nialpdrome and plaindrome are    and  . See the plaindromes for the symmetric pairs.

The first nialpdromes (in base 10) are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44, 50 more terms

Below, the spiral pattern of nialpdromes up to 10000 . See the page on prime numbers for an explanation and links to similar pictures.

Nialpdromes can also be... (you may click on names or numbers and on + to get more values)