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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

%I

%S 1,2,6,12,75,108,315,184,2205,2680,4840,5304,10712,9912,23160,39664,

%T 725968,1005840,4497072,4502480,18009936,18074320,143972272,144087792,

%U 145697200,145945904,295085808,296316720,592629616,590310000,1180428912

%N 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.

%e 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.

%p 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

%K base,nonn

%O 1,2

%A _Leroy Quet_, Sep 11 2008

%E a(7)-a(18) from _R. J. Mathar_, Sep 17 2008

%E a(19)-a(31) from _Ray Chandler_, Nov 06 2008

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Last modified January 22 07:47 EST 2021. Contains 340360 sequences. (Running on oeis4.)