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A258946 Numbers that can be expressed using only the digits 0 and 1 in no more than three different bases. 1
2, 3, 4, 5, 6, 7, 8, 11, 14, 15, 18, 19, 22, 23, 24, 29, 32, 33, 34, 35, 38, 41, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 63, 66, 67, 70, 71, 74, 75, 76, 77, 78, 79, 83, 86, 87, 88, 89, 92, 95, 96, 97, 98, 99, 102, 103, 104, 105, 106, 107 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All integers n >= 4 may trivially be expressed using only the digits 0 and 1 in three different bases: 2, n-1 (as '11') and n (as '10'). The numbers in this sequence cannot be expressed using only 0 and 1 in any other base.

The only positive integers that may be expressed using only the digits 0 and 1 in fewer than three different bases are 2 and 3, for which the values {2, n-1, n} are not all distinct or are not all valid bases.

An equivalent definition: For each term a(n) of this sequence, there are at most three integers k >= 2 for which a(n) is a sum of distinct nonnegative integer powers of k.

LINKS

Thomas Oléron Evans, Table of n, a(n) for n = 1..10000

Thomas Oléron Evans, Python program

EXAMPLE

5 is a term of the sequence, because 5 may be expressed using only the digits 0 and 1 in precisely three different bases: 2, 4 and 5 (5 is '12' in base 3).

9 is not a term of the sequence, because 9 can be expressed using only the digits 0 and 1 in four different bases: 2, 3, 8, 9 (9 is '100' in base 3).

MAPLE

filter:= proc(n)

  local b;

  for b from 3 to n-2 do

    if max(convert(n, base, b)) <= 1 then return false

    fi

  od:

true

end proc:

select(filter, [$2..1000]); # Robert Israel, Jun 19 2015

PROG

(PARI) is(n)=if(n<2, return(0)); for(b=3, sqrtint(n), if(vecmax(digits(n, b))<2, return(0))); 1 \\ Charles R Greathouse IV, Jun 15 2015

CROSSREFS

Subsequence of A074940.

Cf. A146025, A258107, A005836, A000695, A033042.

Sequence in context: A167211 A067133 A192588 * A008815 A298434 A200371

Adjacent sequences:  A258943 A258944 A258945 * A258947 A258948 A258949

KEYWORD

nonn,base

AUTHOR

Thomas Oléron Evans, Jun 15 2015

STATUS

approved

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Last modified January 19 02:30 EST 2022. Contains 350464 sequences. (Running on oeis4.)