

A055085


Smallest integer containing all digits in all bases from 2 to n.


1



2, 11, 75, 978, 8350, 160773, 2217404, 45623244, 1093265784, 37206483195, 1587937206284, 109746121381518, 2697545063614180, 64810523515743579, 21538286780426129155
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

a(12) is the first entry whose expansion in base n does not begin with a 1.  Tom Womack.
By definition, for n>=3, a(n) > A000169(n), with equality when n=2 only.  Michel Marcus, Nov 10 2013
a(16) is the first entry which is bigger than n^n, i.e. whose expansion in base n=16 is not a permutation of 16 different digits.  Ignat Soroko, Aug 14 2017


LINKS

Table of n, a(n) for n=2..16.
Project Euler, Problem 571: Super Pandigital Numbers


EXAMPLE

75 is the smallest integer containing 0 and 1 in base 2 (1001011), 0, 1 and 2 in base 3 (2210) and 0, 1, 2 and 3 in base 4 (1023), hence a(4) = 75
a(12) = 1587937206284 is 217904B5A638 in base 12; 562493178A90 in base 11.


PROG

(PARI) isok(i, n) = {for (b = 2, n, if (#Set(digits(i, b)) != b, return (0)); ); return (1); }
a(n) = {i = n^(n1); while (! isok(i, n), i++); i; } \\ Michel Marcus, Nov 10 2013


CROSSREFS

A051640 uses a weaker definition.
Sequence in context: A112894 A220878 A049363 * A209101 A118802 A053481
Adjacent sequences: A055082 A055083 A055084 * A055086 A055087 A055088


KEYWORD

nonn,base


AUTHOR

Ulrich Schimke (ulrschimke(AT)aol.com)


EXTENSIONS

a(11) from David Wasserman, Mar 25 2002
a(12) from Tom Womack (tom(AT)womack.net), Jun 19 2007
a(13)a(15) from Ignat Soroko, Jan 05 2017
a(16) from Ignat Soroko, Aug 14 2017


STATUS

approved



