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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^(n-1); 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

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Last modified April 9 14:02 EDT 2020. Contains 333353 sequences. (Running on oeis4.)