A394317 Concatenated permutations of integers in decimal.

0, 1, 10, 12, 21, 102, 120, 201, 210, 123, 132, 213, 231, 312, 321, 1023, 1032, 1203, 1230, 1302, 1320, 2013, 2031, 2103, 2130, 2301, 2310, 3012, 3021, 3102, 3120, 3201, 3210, 1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321

Offset

1,3

Comments

The terms of the n-th row of the triangle are the n! concatenations of each permutation of 0, ..., n-1.

Starting with row 11, each concatenated term involves at least one number with more than one digit (see example).

Links

Rhys Evans, Table of n, a(n) for n = 1..10000

Rhys Evans, Plot of first 153 terms

Rhys Evans, Typescript program for OEIS A394317

Example

The triangle starts:
0;
(0)1, 10;
(0)12, (0)21, 102, 120, 201, 210;
...
Row 11 starts:
(0)12345678910, (0)12345678109, (0)12345679810, ... .

Prog

// Typescript (see linked file)
(Python)
from itertools import count, islice, permutations
def a(): yield from (int("".join(map(str, p))) for n in count(1) for p in permutations(range(n)))
print(list(islice(a(), 57))) # Michael S. Branicky, Mar 15 2026

Crossrefs

Cf. A030299.

A precursor of A215940.

Sequence in context: A385154 A348056 A120001 * A108703 A098785 A022324

Adjacent sequences: A394314 A394315 A394316 * A394318 A394319 A394320

Keyword

base,easy,nonn,tabf

Author

Rhys Evans, Mar 15 2026

Status

approved