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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

%I

%S 19,20842,4387884733,301083852338952371,10372871309299412994565980691,

%T 257810894191937039020949293796466032151538,

%U 6291283822228991408060146690794416231996294644948906012153,196933489270977741064964174271054692081510750312035993579769632880958095885917

%N Smallest positive integer k such that k contains all possible pairs of digits when represented in base b = n >= 2.

%C 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.

%H Anthony Sand, <a href="/A249907/b249907.txt">Table of n, a(n) for n = 2..40</a>

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

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

%e 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.

%e 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].

%Y Cf. A033008, A043291.

%K nonn,base

%O 2,1

%A _Anthony Sand_, Nov 08 2014

%E Edited: minor changes in the name, comment and example. - _Wolfdieter Lang_, Nov 21 2014

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Last modified April 21 15:55 EDT 2021. Contains 343156 sequences. (Running on oeis4.)