A187614 Primes p such that the decimal representation of 1/p does not contain every digit 0-9.

2, 3, 5, 7, 11, 13, 31, 37, 41, 43, 67, 73, 79, 101, 137, 239, 271, 353, 449, 757, 859, 1933, 4649, 8779, 9091, 9901, 21401, 21649, 25601, 27961, 52579, 62003, 123551, 333667, 513239, 538987, 909091, 1676321, 2071723, 2906161, 5882353, 10838689, 35121409, 52986961, 99990001, 265371653, 1056689261, 1058313049, 1360682471

Offset: 1

Author

Michel Lagneau, Mar 12 2011

Keywords

• nonn
• base

Comments

Every repunit prime (A004022) is here. There are 113 terms of A046107, having periods of up to 256, that are here. The only known unique-period prime (A007615) not here is the one having period 92092. Is this sequence finite? - T. D. Noe, Mar 13 2011

Examples

			4649 is in the sequence because 1/4649 = 0.00021510002151000215.... contain
  only the digits 0, 1, 2 and 5.
		

Crossrefs

Cf. A187372.

Cf. A352023 (does not contain digit 9)

Programs

Mathematica

Join[{2, 3, 5}, Select[Prime[Range[4, 10000]], Length[Union[RealDigits[1/#][[1, 1]]]] < 10 &]]

Python

from sympy import n_order, nextprime
from itertools import islice
def A187614_gen(): # generator of terms
    yield from (2,3,5)
    p = 7
    while True:
        if len(set('0'+str(10**(n_order(10, p))//p))) < 10:
            yield p
        p = nextprime(p)
A187614_list = list(islice(A187614_gen(),20)) # Chai Wah Wu, Mar 03 2022

Extensions

Extended by T. D. Noe, Mar 12 2011