A144144 a(n) = smallest positive multiple of n that, when represented in binary, contains the binary representations of all positive integers <= n at least once each.

1, 2, 6, 12, 75, 108, 315, 184, 2205, 2680, 4840, 5304, 10712, 9912, 23160, 39664, 725968, 1005840, 4497072, 4502480, 18009936, 18074320, 143972272, 144087792, 145697200, 145945904, 295085808, 296316720, 592629616, 590310000, 1180428912

Offset

1,2

Links

Table of n, a(n) for n=1..31.

Example

5*15 = 75, which is 1001011 in binary. 1 (1 in decimal) occurs like this: (1)001011. 10 (2 in decimal) occurs like this: (10)01011. 11 (3 in decimal) occurs like this: 10010(11). 100 (4 in decimal) occurs like this: (100)1011. And 101 (5 in decimal) occurs like this: 100(101)1. No other smaller positive multiple of 5 contains all the binary representations of the integers 1 to 5. So a(5) = 75.

Maple

A144144 := proc(n) local aprev, k, gooda, a, ntst ; ntst := [seq(convert(i, base, 2), i=1..n)] ; for k from 1 do a := n*k ; gooda := true ; for i from 1 to n do if not verify(convert(a, base, 2), op(i, ntst), 'superlist') then gooda := false ; break ; fi; od: if gooda then RETURN(a) ; fi; od: end: for n from 1 to 40 do printf("%d, ", A144144(n)) ; od: # R. J. Mathar, Sep 17 2008

Crossrefs

Sequence in context: A173843 A107763 A166470 * A226178 A129085 A274941

Adjacent sequences: A144141 A144142 A144143 * A144145 A144146 A144147

Keyword

base,nonn

Author

Leroy Quet, Sep 11 2008

Extensions

a(7)-a(18) from R. J. Mathar, Sep 17 2008

a(19)-a(31) from Ray Chandler, Nov 06 2008

Status

approved