

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
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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..16.
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 Cf. A045572 A002329
Sequence in context: A136895 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


STATUS

approved



