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A079339
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Least k such that the decimal representation of k*n contains only 1's and 0's.
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19
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Contribution 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)
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1999 (derived from A004290)
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FORMULA
| a(n) = A004290(n)/n.
a(n) < 10^(n+1) / (9n). [Charles R Greathouse IV, Jan 09 2012]
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EXAMPLE
| 3*37=111 and no integer k<37 has this property, hence a(3)=37
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PROG
| (PARI) d(n, i)=floor(n/10^(i-1))-10*floor(n/10^i); test(n)=sum(i=1, ceil(log(n)/log(10)), if(d(n, i)*(1-d(n, i)), 1, 0)); a(n)=if(n<0, 0, s=1; while(test(n*s)>0, s++); s)
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CROSSREFS
| Cf. A004290, A070189, A078241-A078248, A096681-A096688.
Sequence in context: A174507 A119483 A157809 * A043075 A106129 A096673
Adjacent sequences: A079336 A079337 A079338 * A079340 A079341 A079342
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KEYWORD
| base,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 13 2003
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs) and Matthew Vandermast (ghodges14(AT)comcast.net), Feb 14 2003
Definition simplified by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 09 2012
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