A144098 a(1)=1. a(n) = the smallest positive multiple of a(n-1) that contains the binary representations of all positive integers <= n at least once each in its binary representation.

1, 2, 6, 12, 108, 108, 756, 1512, 37800, 37800, 945000, 945000, 945000, 945000, 10395000, 20790000, 602910000, 23513490000, 23513490000, 23513490000, 23513490000, 23513490000, 23513490000, 23513490000, 23513490000

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Example

a(4) = 12. Checking the multiples of 12 to see when 1,2,3,4,5 (1,10,11,100,101 in binary) first all occur: 12*1 = 12 = 1100 in binary, contains 1, 2(10 in binary), 3(11 in binary), 4(100 in binary), but not 5(101 in binary). 12*2=24 = 11000 in binary, contains 1 through 4, but not 5. 12*3 = 36 = 100100 in binary, doesn't contain 3(11) or 5(101). 12*4 = 48 = 110000 in binary, doesn't contain 5. 12*5=60 =111100 in binary, doesn't contain 5. 12*6 = 72 = 1001000 in binary, doesn't contain 3 or 5. 12*7= 84 = 1010100 in binary, does not contain 3. 12*8 = 96 = 1100000 in binary, doesn't contain 5. But 12*9 = 108 = 1101100 in binary: Contains 1, like so (1)101100; contains 2, like so 1(10)1100; contains 3, (11)01100; contains 4, 1101(100); and contains 5, 1(101)100. So a(5) = 108.

Maple

A144098 := proc(n) option remember ; local aprev, k, gooda, a, ntst ; if n = 1 then RETURN(1) ; fi; aprev := procname(n-1) ; for k from 1 do a := aprev*k ; gooda := true ; for ntst from 1 to n do if not verify(convert(a, base, 2), convert(ntst, base, 2), 'superlist') then gooda := false ; break ; fi; od: if gooda then RETURN(a) ; fi; od: end: for n from 1 to 40 do printf("%d, ", A144098(n)) ; od: # R. J. Mathar, Sep 17 2008

Crossrefs

Cf. A144099.

Sequence in context: A274941 A141288 A038787 * A259140 A075071 A250269

Adjacent sequences: A144095 A144096 A144097 * A144099 A144100 A144101

Keyword

base,nonn

Author

Leroy Quet, Sep 10 2008

Extensions

More terms from R. J. Mathar, Sep 17 2008

Status

approved