A175557 Prime preperiodic part of the decimal expansion of 1/k as k runs through A065502.

5, 2, 5, 41, 3, 2, 2, 2, 17, 13, 11, 89, 7, 5, 5, 5, 41, 3, 3, 347, 3, 3, 3, 29, 2, 2, 2, 2, 26041, 2, 2, 2, 23, 2, 2, 2, 2, 2, 17, 13, 13, 1201, 11, 11, 107, 919, 89, 7, 7, 7, 7, 7, 7, 61, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 41, 4111, 3

Offset: 1

Author

Michel Lagneau, Jun 30 2010

Keywords

• nonn
• base

Comments

Primes in A175555 in the order of appearance.

Multiples of 2 or 5 generate a quotient with a preperiodic sequence of digits, for example 1/24 = 0.041666666..., and 41 is the decimal form of the preperiodic part.

The corresponding values of n are: 2, 5, 20, 24, 28, 36, 44, 50, 56, 72, 88, 112, 136, 168, 184, ...

Examples

			The prime 347 is in the sequence because 1/288 = .00347222222222222222...
The prime 1201 is in the sequence because 1/832 =.001201 923076 923076 ...
		

References

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

Crossrefs

Cf. A175555, A036275, A065502.

Programs

Maple

for n from 1 do
    p := A175555(n) ;
    if isprime(p) then
        print(p) ;
    end if;
end do: # R. J. Mathar, Jul 22 2012