

A131646


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


5



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

1,3


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), 174179.


LINKS

Table of n, a(n) for n=1..20.
Daniel Mondot, Related Puzzle.


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 *)


PROG

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


CROSSREFS

Cf. A146025, A146026, A146027, A146028, A146029.
Sequence in context: A048408 A199343 A118765 * A032864 A032888 A023791
Adjacent sequences: A131643 A131644 A131645 * A131647 A131648 A131649


KEYWORD

nonn,base


AUTHOR

Daniel Mondot, Sep 08 2007, Nov 02 2008


EXTENSIONS

Edited by Charles R Greathouse IV, Nov 01 2009
Reference added by William Rex Marshall, Oct 23 2011


STATUS

approved



