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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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33
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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
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OFFSET
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1,2
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COMMENTS
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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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REFERENCES
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Popular Computing (Calabasas, CA), Z-Sequences, Vol. 4 (No. 34, A pr 1976), pages PC36-4 to PC37-6, but there are many errors (cf. A257343, A257344).
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LINKS
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FORMULA
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EXAMPLE
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3*37 = 111 and no integer k < 37 has this property, hence a(3)=37.
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PROG
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(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
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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