|
Search: id:A144144
|
|
|
| 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. |
|
+0
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
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
Leroy Quet, Home Page (listed in lieu of email address)
|
|
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: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008]
|
|
CROSSREFS
|
Sequence in context: A076220 A107763 A166470 this_sequence A129085 A141288 A062954
Adjacent sequences: A144141 A144142 A144143 this_sequence A144145 A144146 A144147
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
Leroy Quet Sep 11 2008
|
|
EXTENSIONS
|
a(7)-a(18) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008
a(19)-a(31) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 06 2008
|
|
|
Search completed in 0.005 seconds
|
