OFFSET
1,1
COMMENTS
This sequence is infinite because the numbers 3, 33, 333, ... generate the decimal form 3. The correspondant primes of this sequence such that :
{3, 37, 3, 3, 271, 11, 4649, 41, 333667, 3} are included in the sequence A178505.
The Maple program below is very slow for the numbers > 3333.
REFERENCES
H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, 'Die periodischen Dezimalbrueche'.
LINKS
EXAMPLE
27 is in the sequence because 1/27 = 0.037 037 ... and 37 is prime.
2997 is in the sequence because 1/2997 = 0.000333667 000333667 ... and 333667 is prime.
MAPLE
with(numtheory): Digits:=4000:nn:=4000:for n from 3 by 2 to nn do:z:=evalf(1/n): indic:=0:for p from 1 to nn do:if irem(10^p, n) = 1 and gcd(n, 5) = 1 and indic=0 then pp:=p:indic:=1:z1:=floor(z*10^pp): else fi:od:if indic=1 and type(z1, prime)=true then print(n):else fi:od:
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Jun 24 2010
EXTENSIONS
Extended and name corrected by T. D. Noe, Nov 18 2010
a(17)-a(20) from Ray Chandler, Apr 17 2017
STATUS
approved