

A079339


Least k such that the decimal representation of k*n contains only 1's and 0's.


32



1, 5, 37, 25, 2, 185, 143, 125, 12345679, 1, 1, 925, 77, 715, 74, 625, 653, 61728395, 579, 5, 481, 5, 4787, 4625, 4, 385, 40781893, 3575, 37969, 37, 3581, 3125, 3367, 3265, 286, 308641975, 3, 2895, 259, 25, 271, 2405, 25607, 25, 24691358, 23935, 213, 23125
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OFFSET

1,2


COMMENTS

From David Amar (dpamar(AT)gmail.com), Jul 12 2010: (Start)
This sequence is well defined.
In the n+1 first repunits (see A002275), there are at least 2 numbers that have the same value modulo n (Pigeonhole principle).
The difference between those two numbers contains only 1's and 0's in decimal representation. (End)


REFERENCES

Popular Computing (Calabasas, CA), ZSequences, Vol. 4 (No. 34, A pr 1976), pages PC364 to PC376, but there are many errors (cf. A257343, A257344).


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..10000 First 1999 terms from T. D. Noe and the next 7999 terms from N. J. A. Sloane [Based on A004290].


FORMULA

a(n) = A004290(n)/n.
a(n) < 10^(n+1) / (9n).  Charles R Greathouse IV, Jan 09 2012


EXAMPLE

3*37=111 and no integer k<37 has this property, hence a(3)=37.


PROG

(PARI) d(n, i)=floor(n/10^(i1))10*floor(n/10^i); test(n)=sum(i=1, ceil(log(n)/log(10)), if(d(n, i)*(1d(n, i)), 1, 0)); a(n)=if(n<0, 0, s=1; while(test(n*s)>0, s++); s)


CROSSREFS

Cf. A004290, A070189, A078241A078248, A096681A096688, A257343, A257344, A257345.
Sequence in context: A174507 A119483 A157809 * A257343 A244927 A043075
Adjacent sequences: A079336 A079337 A079338 * A079340 A079341 A079342


KEYWORD

base,nonn


AUTHOR

Benoit Cloitre, Feb 13 2003


EXTENSIONS

More terms from Vladeta Jovovic and Matthew Vandermast, Feb 14 2003
Definition simplified by Franklin T. AdamsWatters, Jan 09 2012


STATUS

approved



