A033008 -id:A033008 - cp's OEIS frontend

A043314 a(n)=A033008(n)/11.

1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 102, 103, 104, 105, 106, 107, 108, 109, 200, 201, 203, 204, 205, 206, 207, 208, 209, 300, 301, 302, 304, 305, 306, 307, 308, 309, 400, 401, 402, 403, 405, 406, 407, 408, 409, 500, 501, 502, 503, 504

Offset: 1

Clark Kimberling

Also, numbers which, written in base 100, have all digits < 10 and no adjacent digits equal. - M. F. Hasler, Feb 03 2014

Cf. A043307 - A043320, A043291, A033001 - A033014, A033016 - A033029.

is_A043314(n)=(n=[n])&&!until(!n[1],((n=divrem(n[1],100))[2]<10 && n[1]%10!=n[2])||return) \\ M. F. Hasler, Feb 03 2014

A247241 In base 2, smallest positive integer k such that k contains all possible strings of n binary digits.

Original entry on oeis.org

2, 19, 558, 272060, 34949682936, 297564712194085870576, 10932581082490851526951746612437309648864, 7425338450010038712278392695279246718801455644988538421150211866664645481447360

Offset: 1

Anthony Sand, Nov 28 2014

In base 2, there are 2^n distinct strings of n digits and the smallest positive integer to contain all of them will have 2^n+(n-1) digits (see A052944). For example, there are 2^2 = 4 distinct strings of two digits: 00, 01, 10, 11. All of them are represented in the 5-digit binary number 10011 = 19 in base 10.

			n = 1: a(1) = 2 = 10 in base 2, which contains 2 distinct strings of one digit: 1, 0.
n = 2: a(2) = 19 = 10011, which contains 4 distinct strings of two digits: 10, 00, 01, 11.
n = 3: a(3) = 558 = 1000101110, which contains 8 distinct strings of three digits: 100, 000, 001, 010, 101, 011, 111, 110.
n = 4: a(4) = 272060 = 1000010011010111100, which contains 16 distinct strings of four digits: 1000, 0000, 0001, 0010, 0100, 1001, 0011, 0110, 1101, 1010, 0101, 1011, 0111, 1111, 1110, 1100.

Anthony Sand, Table of n, a(n) for n = 1..12

Cf. A249907, A033008.

A249907 Smallest positive integer k such that k contains all possible pairs of digits when represented in base b = n >= 2.

Original entry on oeis.org

19, 20842, 4387884733, 301083852338952371, 10372871309299412994565980691, 257810894191937039020949293796466032151538, 6291283822228991408060146690794416231996294644948906012153, 196933489270977741064964174271054692081510750312035993579769632880958095885917

Offset: 2

Anthony Sand, Nov 08 2014

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.

			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].

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

Cf. A033008, A043291.

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

cp's OEIS Frontend

A043314 a(n)=A033008(n)/11.

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A247241 In base 2, smallest positive integer k such that k contains all possible strings of n binary digits.

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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.

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