A242075 - OEIS

A242075

Smallest positive integer divisible by n to occur as the initial digits in the decimal expansion of the reciprocal of n, or 0 if impossible.

1, 50, 3, 2500, 20, 0, 14, 125000, 111111111, 10, 909090909090909090909, 0, 769230769230769230769230769, 714, 0, 6250000, 5882, 0, 5263, 500, 4761904761904761904761904761904761, 454545454, 4347, 0, 400

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OFFSET

1,2

COMMENTS

From Wolfdieter Lang, May 09 2014: (Start)

We consider only the digits after the decimal point, and leading zero digits are ignored. E.g., for 1/200 = .005 one checks 5, 50, 500, ..., for a factor 200, to find 5000/200 = 25, hence a(200) = 5000 = a(20)*10.

The a(n)/n sequence starts 1, 25, 1, 625, 4, 0, 2, 15625, 12345679, 1, 82644628099173553719, 0, 59171597633136094674556213, 51, 0, 390625, 346, 0, 277, 25, 226757369614512471655328798185941, 20661157, 189, 0, 16, ... (End)

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LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

a(4) = 2500 because 1/4=0.25 but cannot be 25 or 250 because they are not divisible by 4.

a(6) = 0 because 1/6=0.1666... and no number made of a 1 and repeating 6's is divisible by 6 (all these numbers are congruent to 4 mod 6).

From Wolfdieter Lang, May 09 2014: (Start)

a(27) = 3703703703703703703703703703703703703703703703703703703703703703703703703,

a(27)/27 = 137174211248285322359396433470507544581618655692729766803840877914951989.

(End)

CROSSREFS

Sequence in context: A337330 A174914 A036172 * A187526 A187697 A048178

Adjacent sequences: A242072 A242073 A242074 * A242076 A242077 A242078

KEYWORD

nonn,base

AUTHOR

J. Lowell, May 03 2014

EXTENSIONS

a(11)..a(25) from Wolfdieter Lang, May 09 2014

a(21) corrected by J. Lowell, May 09 2014

STATUS

approved