A245715 -id:A245715 - cp's OEIS frontend

A245716 Least number k > 0 such that n + k! and n - k! are both prime, or 0 if no such k exists.

0, 0, 0, 1, 2, 1, 0, 0, 2, 0, 3, 1, 3, 0, 2, 0, 3, 1, 0, 0, 2, 0, 3, 0, 3, 0, 0, 0, 4, 1, 0, 0, 0, 0, 3, 0, 3, 0, 2, 0, 0, 1, 4, 0, 2, 0, 3, 0, 0, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 3, 0, 2, 0, 0, 1, 3, 0, 0, 0, 3, 0, 0, 0, 2, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 1, 3, 0, 2, 0, 3, 1, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Derek Orr, Jul 30 2014

nonn

For a(n) > 0, a(n)! < n for all n. Thus a(n) = 0 is definite.

			13 + 1! and 13 - 1! are not both prime.
13 + 2! and 13 - 2! are not both prime.
13 + 3! and 13 - 3! are both prime (19 and 7). Thus a(13) = 3.

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A245714, A245715.

a(n)=for(k=1,n,if(ispseudoprime(n-k!)&&ispseudoprime(n+k!),return(k)))
vector(150,n,a(n))

A241424 Largest number k > 0 such that n - k! is prime, or 0 if no such k exists.

Original entry on oeis.org

0, 0, 1, 2, 2, 1, 2, 3, 3, 0, 3, 1, 3, 1, 2, 0, 3, 1, 3, 1, 2, 0, 3, 1, 3, 4, 4, 0, 4, 1, 4, 1, 2, 0, 4, 0, 4, 1, 2, 0, 4, 1, 4, 1, 2, 0, 4, 1, 3, 0, 0, 0, 4, 1, 4, 0, 0, 0, 3, 1, 4, 1, 2, 0, 4, 0, 4, 1, 2, 0, 4, 1, 3, 1, 2, 0, 4, 0, 3, 1, 2, 0, 4, 1, 4, 0, 0, 0, 3, 1, 4, 0, 0, 0, 4

Offset: 1

Derek Orr, Aug 08 2014

nonn

If k > n, n - k! is negative and therefore, not prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A175940, A245715.

a:= proc(n) local k, r;
r:= 0;
for k from 1 do
   if k! >= n then return r
   elif isprime(n-k!) then r:= k
   fi
od
end proc:
seq(a(n),n=1..100); # Robert Israel, Aug 10 2014

a[n_] := Module[{k, r = 0}, For[k = 1, True, k++, If[k! >= n, Return[r], If[PrimeQ[n - k!], r = k]]]];
Array[a, 100] (* Jean-François Alcover, Jul 27 2020, after Maple *)

a(n)=forstep(k=n,1,-1,if(ispseudoprime(n-k!),return(k)))
n=1;while(n<150,print1(a(n),", ");n++)

cp's OEIS Frontend

A245716 Least number k > 0 such that n + k! and n - k! are both prime, or 0 if no such k exists.

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