A179192 Numbers n, not relatively prime to 10, such that the decimal form of the period of 1/n is prime.

12, 18, 30, 36, 45, 48, 75, 120, 180, 192, 198, 270, 288, 300, 330, 360, 450, 480, 495, 750, 768, 1152, 1200, 1584, 1800, 1875, 1920, 1980, 1998, 2304, 2700, 2880, 3000, 3072, 3300, 3330, 3600, 3690, 4500, 4800, 4950, 4995, 5625, 7500, 7680, 9090, 11520, 12000, 12288, 15840, 18000, 18432, 18750, 19200, 19800, 19980, 19998

Offset

1,1

Comments

The sequence A175545 (numbers n such that the decimal form of the period of 1/n is prime) is only concerned with numbers n such that gcd(n,10)=1. Each number n such that gcd(n,10)<>1 generates a quotient where there exist a sequence of digits which is periodic after a finite sequence of digits, for example 1/36 = .0277777.... and 7 is periodic.

The prime numbers corresponding to this sequence are :

3, 5, 3, 7, 2, 3, 3, 3, 5, 3, 5, 37, 2, 3, 3, 7, 2, 3, 2,...

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..57.

Formula

Union of A179192 and A175545 is A061564.

Example

1584 is in the sequence because 1/1584 = .0006313131313131313131... and 31 is prime.

Mathematica

Reap[Do[p=RealDigits[1/n][[1, -1]]; If[GCD[10, n]>1 && Head[p] === List, While[p[[-1]] == 0, p=Most[p]]; If[PrimeQ[FromDigits[p]], Sow[n]]], {n, 20000}]][[2, 1]]

Crossrefs

Cf. A175557, A175555, A178505, A045572, A002329

Sequence in context: A006622 A124269 A361080 * A344198 A112054 A225576

Adjacent sequences: A179189 A179190 A179191 * A179193 A179194 A179195

Keyword

nonn,base

Author

Michel Lagneau, Jul 01 2010

Extensions

Sequence corrected by T. D. Noe, Nov 18 2010

Status

approved