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A116898
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Numbers k such that k! is turned into a prime number by changing its trailing 0's into 1's.
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0
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OFFSET
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1,1
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COMMENTS
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Also numbers k such that n! + R(Z(k)) is prime, where R(t) = (10^t - 1)/9 is the repunit with t digits (A002275) and Z(m) = Sum_{j>=1} floor(m/5^j) is the number of trailing zeros of m! (A027868). The (probable) prime corresponding to a(5)=1746 has 4905 digits. Next term must be greater than 4000.
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LINKS
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EXAMPLE
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10 is a term, since 10! = 3628800 and 3628811 is prime.
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MAPLE
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q:= n-> (f-> isprime(f+(10^padic[ordp](f, 10)-1)/9))(n!):
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MATHEMATICA
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tz1Q[n_]:=Module[{idn=Split[IntegerDigits[n!]]}, PrimeQ[ FromDigits[ Flatten[ Join[ Most[ idn], Last[idn]/.(0->1)]]]]]; Select[ Range[ 1800], tz1Q] (* Harvey P. Dale, Oct 01 2015 *)
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PROG
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(Python)
from sympy import isprime
from math import factorial
def ok(n):
s, zeros = str(factorial(n)), 0
while s[-1] == '0': s = s[:-1]; zeros += 1
return isprime(int(s + '1'*zeros))
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CROSSREFS
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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STATUS
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approved
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