A061564 -id:A061564 - cp's OEIS frontend

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

Michel Lagneau, Jul 01 2010

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,...

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

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

Cf. A175557, A175555, A178505, A045572, A002329

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]]

Union of A179192 and A175545 is A061564.

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

cp's OEIS Frontend

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

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