A number is a plaindrome
in a given base
(often 10 or 16)
if its digits are in nondecreasing order in that base.
For example, 1234, 2222, 25667 and 2468 are all plaindromes in base 10.
Clearly a plaindrome cannot contain the digit 0, unless it is the number 0 itself, so the plaindromes in base 2 correspond to numbers of the form , i.e., to numbers of the form .
A plaindrome in which the digits are strictly increasing is called
metadrome, while numbers whose digits are nonincreasing and
strictly decreasing are called nialpdromes and
The number of plaindromes of digits in base is equal to
collapses to 1, and for
. In general
, since we count also the 0 among the 1-digit plaindromes.
The total number of plaindromes in base
with at most digits is equal to
Probably the largest plaindrome primes with index respectively
plaindrome and nialdrome are and .
See the nialpdromes for the symmetric pair.
The first plaindromes (in base 10) are 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22 more terms
Below, the spiral pattern of plaindromes in base 10 up to 4900. 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 plaindromes are multiples of the primes p
from 2 to 71. In black the ideal line 1/p