A131646 Numbers that can be written from base 2 to base 18 using only the digits 0 to 9 (conjectured to be complete).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 20, 1027, 1028, 1029, 14745, 9020076688681, 9439828025162228377, 9439829801208141318

Offset: 1

Author

Daniel Mondot, Sep 08 2007, Nov 02 2008

Keywords

• nonn
• base

Comments

Originally checked to 2^20356 (or 5.8*10^6127) in Nov 2008.

It appears that 19 and 20 are the only numbers > 9 that can be written up to base 19 only using digits 0 to 9 and 20 is the only number > 9 that can be written up to base 20 only using digits 0 to 9.

It is a plausible conjecture that there are no more terms, but this has not been proved. - N. J. A. Sloane, Nov 17 2017

References

• B. R. Barwell, Numbers Without Letters, Journal of Recreational Mathematics, Vol. 25:3 (1993), 174-179.

Links

• Daniel Mondot, Related Puzzle.

Crossrefs

Cf. A146025, A146026, A146027, A146028, A146029.

Programs

Mathematica

f[n_] := Total[Total@ Drop[RotateRight[DigitCount[n, #]], 10] & /@ Range[11, 18]]; Select[Range[0, 20000], f@ # == 0 &] (* Michael De Vlieger, Aug 29 2015 *)

PARI

isok(n) = if (n, for (b=11, 18, if (vecmax(digits(n,b))>9, return(0)))); 1; \\ Michel Marcus, Aug 30 2015

Extensions

Edited by Charles R Greathouse IV, Nov 01 2009

Reference added by William Rex Marshall, Oct 23 2011