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A179192
Numbers n, not relatively prime to 10, such that the decimal form of the period of 1/n is prime.
1
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'.
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
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Jul 01 2010
EXTENSIONS
Sequence corrected by T. D. Noe, Nov 18 2010
STATUS
approved