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

%I A187614 #33 Mar 05 2022 14:18:08
%S A187614 2,3,5,7,11,13,31,37,41,43,67,73,79,101,137,239,271,353,449,757,859,
%T A187614 1933,4649,8779,9091,9901,21401,21649,25601,27961,52579,62003,123551,
%U A187614 333667,513239,538987,909091,1676321,2071723,2906161,5882353,10838689,35121409,52986961,99990001,265371653,1056689261,1058313049,1360682471
%N A187614 Primes p such that the decimal representation of 1/p does not contain every digit 0-9.
%C A187614 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
%e A187614 4649 is in the sequence because 1/4649 = 0.00021510002151000215.... contain
%e A187614   only the digits 0, 1, 2 and 5.
%t A187614 Join[{2, 3, 5}, Select[Prime[Range[4, 10000]], Length[Union[RealDigits[1/#][[1, 1]]]] < 10 &]]
%o A187614 (Python)
%o A187614 from sympy import n_order, nextprime
%o A187614 from itertools import islice
%o A187614 def A187614_gen(): # generator of terms
%o A187614     yield from (2,3,5)
%o A187614     p = 7
%o A187614     while True:
%o A187614         if len(set('0'+str(10**(n_order(10, p))//p))) < 10:
%o A187614             yield p
%o A187614         p = nextprime(p)
%o A187614 A187614_list = list(islice(A187614_gen(),20)) # _Chai Wah Wu_, Mar 03 2022
%Y A187614 Cf. A187372.
%Y A187614 Cf. A352023 (does not contain digit 9)
%K A187614 nonn,base
%O A187614 1,1
%A A187614 _Michel Lagneau_, Mar 12 2011
%E A187614 Extended by _T. D. Noe_, Mar 12 2011