A175545 Numbers n (relatively prime to 10) such that the decimal form of the period of 1/n is prime.

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

Offset: 1

Author

Michel Lagneau, Jun 24 2010

Keywords

• nonn
• base

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.

Examples

			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.
		

References

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

Links

• Index entries for sequences related to decimal expansion of 1/n.

Crossrefs

Cf. A178505, A045572, A002329.

Programs

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:

Extensions

Extended and name corrected by T. D. Noe, Nov 18 2010

a(17)-a(20) from Ray Chandler, Apr 17 2017