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plaindromes
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 katadromes.

The number    of plaindromes of    digits in base    is equal to

which, for    collapses to 1, and for    simplifies to  . 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.

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