

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



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
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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



