A352023 Primes p such that 1/p does not contain digit '9' in its decimal expansion.
2, 3, 5, 7, 37, 79, 239, 4649, 62003, 538987, 35121409, 265371653
Offset: 1
Examples
The largest digit in the decimal expansion of 1/7 = 0.142857142857... is 8 < 9, hence 7 is a term.
Programs
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Maple
f:= proc(n) local m, S, r; m:= 1; S:= {1}; do r:= floor(m/n); if r = 9 then return true fi; m:= (m - r*n)*10; if member(m, S) then return false fi; S:= S union {m}; od end proc: remove(f, [seq(ithprime(i),i=1..10^5)]); # Robert Israel, Mar 16 2022 -
Mathematica
Select[Range[10^5], PrimeQ[#] && FreeQ[RealDigits[1/#][[1, 1]], 9] &] (* Amiram Eldar, Feb 28 2022 *)
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PARI
isok(p) = if (isprime(p), my(m2=valuation(p, 2), m5=valuation(p, 5)); vecmax(digits(floor(10^(max(m2,m5) + znorder(Mod(10, p/2^m2/5^m5))+1)/p))) < 9); \\ Michel Marcus, Feb 28 2022
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Python
from sympy import n_order, nextprime from itertools import islice def A352023_gen(): # generator of terms yield from (2,3,5) p = 7 while True: if '9' not in str(10**(n_order(10, p))//p): yield p p = nextprime(p) A352023_list = list(islice(A352023_gen(),9)) # Chai Wah Wu, Mar 03 2022
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