%I
%S 12,18,30,36,45,48,75,120,180,192,198,270,288,300,330,360,450,480,495,
%T 750,768,1152,1200,1584,1800,1875,1920,1980,1998,2304,2700,2880,3000,
%U 3072,3300,3330,3600,3690,4500,4800,4950,4995,5625,7500,7680,9090,11520,12000,12288,15840,18000,18432,18750,19200,19800,19980,19998
%N Numbers n, not relatively prime to 10, such that the decimal form of the period of 1/n is prime.
%C 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.
%C The prime numbers corresponding to this sequence are :
%C 3, 5, 3, 7, 2, 3, 3, 3, 5, 3, 5, 37, 2, 3, 3, 7, 2, 3, 2,...
%D H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, 'Die periodischen Dezimalbrueche'.
%F Union of A179192 and A175545 is A061564.
%e 1584 is in the sequence because 1/1584 = .0006313131313131313131... and 31 is prime.
%t 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]]
%Y Cf. A175557, A175555, A178505, A045572, A002329
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Jul 01 2010
%E Sequence corrected by _T. D. Noe_, Nov 18 2010
