Search: id:A144144
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%I A144144
%S A144144 1,2,6,12,75,108,315,184,2205,2680,4840,5304,10712,9912,23160,39664,
%T A144144 725968,1005840,4497072,4502480,18009936,18074320,143972272,144087792,
%U A144144 145697200,145945904,295085808,296316720,592629616,590310000,1180428912
%N A144144 a(n) = smallest positive multiple of n which when represented in binary 
               contains the binary representations of all positive integers <= n 
               at least once each.
%H A144144 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A144144 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 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: [From 
               R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008]
%Y A144144 Sequence in context: A076220 A107763 A166470 this_sequence A129085 A141288 
               A062954
%Y A144144 Adjacent sequences: A144141 A144142 A144143 this_sequence A144145 A144146 
               A144147
%K A144144 base,nonn
%O A144144 1,2
%A A144144 Leroy Quet Sep 11 2008
%E A144144 a(7)-a(18) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008
%E A144144 a(19)-a(31) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 06 
               2008

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