

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.


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

fini,full,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



