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A241423
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Largest number k > 0 such that n + k! is prime, or 0 if no such k exists.
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2
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1, 2, 1, 4, 1, 6, 0, 2, 1, 10, 1, 6, 0, 2, 1, 11, 1, 14, 0, 2, 1, 16, 0, 3, 0, 2, 1, 20, 1, 22, 0, 0, 0, 4, 1, 33, 0, 2, 1, 25, 1, 38, 0, 2, 1, 44, 0, 6, 0, 2, 1, 52, 0, 4, 0, 2, 1, 27, 1, 50, 0, 0, 0, 4, 1, 64, 0, 2, 1, 55, 1, 67, 0, 0, 0, 6, 1, 73, 0, 2, 1, 68, 0, 4, 0, 2, 1, 52, 0, 6
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OFFSET
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2,2
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COMMENTS
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If k >= n, then n + k! is divisible by n and is not prime.
a(n) < A020639(n), because if prime p divides n then p divides n + k! for k >= p. - Robert Israel, Aug 10 2014
There is no term for n = 1 since factorial primes 1 + k! can probably be arbitrarily large (A002981 shows k values). - Jens Kruse Andersen, Aug 13 2014
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LINKS
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MAPLE
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a:= proc(n)
local k;
for k from min(numtheory:-factorset(n)) to 1 by -1 do
if isprime(n+k!) then return(k) fi
od:
0
end proc:
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MATHEMATICA
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a[n_] := Module[{k}, For[k = FactorInteger[n][[1, 1]], k >= 1, k--, If[PrimeQ[n + k!], Return[k]]]; 0];
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PROG
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(PARI)
a(n)=forstep(k=n, 1, -1, if(ispseudoprime(n+k!), return(k)))
n=2; while(n<150, print1(a(n), ", "); n++)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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