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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 (list; graph; refs; listen; history; text; internal format)
 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 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: A071354 A006622 A124269 * A112054 A225576 A275082 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

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