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

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

Offset

1,1

Comments

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.

Links

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

Example

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.

Crossrefs

Cf. A249907, A033008.

Sequence in context: A306457 A158099 A015204 * A270918 A296235 A290302

Adjacent sequences: A247238 A247239 A247240 * A247242 A247243 A247244

Keyword

nonn,base

Author

Anthony Sand, Nov 28 2014

Status

approved