

A258107


Smallest number > 1 whose representation in all bases up to n consists only of zeros and ones.


3




OFFSET

2,1


COMMENTS

As with A146025, it is a plausible conjecture that there are no more terms, but this has not been proved.  Daniel Mondot, Dec 16 2016


LINKS

Table of n, a(n) for n=2..5.
Thomas OlĂ©ron Evans, Solution: Covering all the bases
Richard Green, A Curious Property of 82000
James Grime and Brady Haran, Why 82,000 is an extraordinary number, Numberphile video, 2015.


EXAMPLE

a(4) = 4 because it is 100 in base 2, 11 in base 3 and 10 in base 4. No smaller number, except 1, can be expressed in such bases with only zeros and ones.
a(5) = 82000: 82000 in bases 2 through 5 is 10100000001010000, 11011111001, 110001100, 10111000, containing only 0s and 1s, while all smaller numbers have a larger digit in one of those bases. For example, 12345 is 11000000111001, 121221020, 3000321, 343340.  N. J. A. Sloane, Feb 01 2016


MATHEMATICA

Table[k = 2; While[Total[Total@ Drop[RotateRight[DigitCount[k, #]], 2] & /@ Range[3, n]] > 0, k++]; k, {n, 2, 5}] (* Michael De Vlieger, Aug 29 2015 *)


CROSSREFS

Cf. A146025.
Sequence in context: A038105 A143716 A228311 * A107656 A024595 A144804
Adjacent sequences: A258104 A258105 A258106 * A258108 A258109 A258110


KEYWORD

nonn,base,more


AUTHOR

Bernardo Boncompagni, May 20 2015


STATUS

approved



