

A175545


Numbers n (relatively prime to 10) such that the decimal form of the period of 1/n is prime.


2



3, 27, 33, 333, 369, 909, 2151, 2439, 2997, 3333, 27027, 33333, 37683, 41841, 76923, 90909, 142857, 194841, 243603, 333333
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OFFSET

1,1


COMMENTS

This sequence is infinite because the numbers 3, 33, 333, ... generate the decimal form 3. The correspondant primes of this sequence such that :
{3, 37, 3, 3, 271, 11, 4649, 41, 333667, 3} are included in the sequence A178505.
The Maple program below is very slow for the numbers > 3333.


REFERENCES

H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, 'Die periodischen Dezimalbrueche'.


LINKS

Table of n, a(n) for n=1..20.
Index entries for sequences related to decimal expansion of 1/n.


EXAMPLE

27 is in the sequence because 1/27 = 0.037 037 ... and 37 is prime.
2997 is in the sequence because 1/2997 = 0.000333667 000333667 ... and 333667 is prime.


MAPLE

with(numtheory): Digits:=4000:nn:=4000:for n from 3 by 2 to nn do:z:=evalf(1/n): indic:=0:for p from 1 to nn do:if irem(10^p, n) = 1 and gcd(n, 5) = 1 and indic=0 then pp:=p:indic:=1:z1:=floor(z*10^pp): else fi:od:if indic=1 and type(z1, prime)=true then print(n):else fi:od:


CROSSREFS

Cf. A178505, A045572, A002329.
Sequence in context: A319391 A034594 A077533 * A032418 A108163 A108114
Adjacent sequences: A175542 A175543 A175544 * A175546 A175547 A175548


KEYWORD

nonn,base


AUTHOR

Michel Lagneau, Jun 24 2010


EXTENSIONS

Extended and name corrected by T. D. Noe, Nov 18 2010
a(17)a(20) from Ray Chandler, Apr 17 2017


STATUS

approved



