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A249907 Smallest positive integer k such that k contains all possible pairs of digits when represented in base b = n >= 2. 2
19, 20842, 4387884733, 301083852338952371, 10372871309299412994565980691, 257810894191937039020949293796466032151538, 6291283822228991408060146690794416231996294644948906012153, 196933489270977741064964174271054692081510750312035993579769632880958095885917 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

In base b, there are b^2 distinct pairs of digits and the smallest positive integer to contain all of them will have (b^2)+1 digits. For example, in base 2 there are 2^2 = 4 distinct pairs: 00, 01, 10, 11. All of them are represented in the 5-digit binary number 10011 = 19 in base 10.

LINKS

Anthony Sand, Table of n, a(n) for n = 2..40

EXAMPLE

n = 2: a(2) = 19 = 10011 in base 2, which contains 4 distinct pairs of digits: 10, 00, 01, 11.

n = 3: a(3) = 20842 = 1001120221 in base 3, which contains 9 distinct pairs of digits: 10, 00, 01, 11, 12, 20, 22, 21.

n = 4: a(4) = 4387884733 = 10011202130322331 in base 4, which contains 16 distinct pairs of digits: 10, 00, 01, 11, 12, 20, 02, 21, 13, 30, 03, 32, 22, 23, 33, 31.

In base 10, all pairs from 00 to 99 are found in the 101 digits of [1, 0, 0, 1, 1, 2, 0, 2, 1, 3, 0, 3, 1, 4, 0, 4, 1, 5, 0, 5, 1, 6, 0, 6, 1, 7, 0, 7, 1, 8, 0, 8, 1, 9, 0, 9, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 5, 5, 6, 5, 7,5, 8, 5, 9, 6, 6, 7, 6, 8, 6, 9, 7, 7, 8, 7, 9, 8, 8, 9, 9, 1].

CROSSREFS

Cf. A033008, A043291.

Sequence in context: A233233 A203581 A125043 * A233105 A013528 A172762

Adjacent sequences:  A249904 A249905 A249906 * A249908 A249909 A249910

KEYWORD

nonn,base

AUTHOR

Anthony Sand, Nov 08 2014

EXTENSIONS

Edited: minor changes in the name, comment and example. - Wolfdieter Lang, Nov 21 2014

STATUS

approved

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Last modified March 6 03:35 EST 2021. Contains 341841 sequences. (Running on oeis4.)