A394317 - OEIS

%I #21 Mar 22 2026 16:05:39

%S 0,1,10,12,21,102,120,201,210,123,132,213,231,312,321,1023,1032,1203,

%T 1230,1302,1320,2013,2031,2103,2130,2301,2310,3012,3021,3102,3120,

%U 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

%N Concatenated permutations of integers in decimal.

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

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

%H Rhys Evans, <a href="/A394317/b394317.txt">Table of n, a(n) for n = 1..10000</a>

%H Rhys Evans, <a href="/A394317/a394317.png">Plot of first 153 terms</a>

%H Rhys Evans, <a href="/A394317/a394317.ts.txt">Typescript program for OEIS A394317</a>

%e The triangle starts:

%e 0;

%e (0)1, 10;

%e (0)12, (0)21, 102, 120, 201, 210;

%e ...

%e Row 11 starts:

%e (0)12345678910, (0)12345678109, (0)12345679810, ... .

%o // Typescript (see linked file)

%o (Python)

%o from itertools import count, islice, permutations

%o def a(): yield from (int("".join(map(str, p))) for n in count(1) for p in permutations(range(n)))

%o print(list(islice(a(), 57))) # _Michael S. Branicky_, Mar 15 2026

%Y Cf. A030299.

%Y A precursor of A215940.

%K base,easy,nonn,tabf

%O 1,3

%A _Rhys Evans_, Mar 15 2026