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
The number of nialpdromes of digits in base is equal 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.
Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
A graph displaying how many nialpdromes are multiples of the primes p
from 2 to 71. In black the ideal line 1/p