OFFSET
1,1
COMMENTS
Terms a(1)-a(9) and a(10)-a(12) were respectively found by Giovanni Resta and Robert Israel (comments in A333237).
The corresponding largest digit in the decimal expansion of 1/a(n) is A352024(n).
If it exists, a(13) > 2.7*10^8.
a(13) > 1360682471 (with A187614). - Jinyuan Wang, Mar 03 2022
a(13) <= 5363222357, a(14) <= 77843839397. - David A. Corneth, Mar 03 2022
EXAMPLE
The largest digit in the decimal expansion of 1/7 = 0.142857142857... is 8 < 9, hence 7 is a term.
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 *)
PROG
(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
(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)
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Bernard Schott, Feb 28 2022
STATUS
approved