A245716 -id:A245716 - cp's OEIS frontend

A241425 Largest 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, 4, 0, 4, 0, 2, 0, 0, 1, 4, 0, 2, 0, 4, 0, 0, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 4, 0, 3, 0, 2, 0, 0, 1, 3, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3

Offset: 1

Derek Orr, Aug 08 2014

nonn

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

a(n) < A020639(n). - Robert Israel, Aug 10 2014

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

Cf. A020639, A245716, A241423, A241424.

a:= proc(n)
local k;
for k from min(numtheory:-factorset(n))-1 to 1 by -1 do
  if n > k! and isprime(n+k!) and isprime(n-k!) then return(k) fi
od:
0
end proc:
a(1):= 0:
seq(a(n),n=1..100); # Robert Israel, Aug 10 2014

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

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

A242040 Numbers n such that n + k! and n - k! are both prime for some k.

Original entry on oeis.org

4, 5, 6, 9, 11, 12, 13, 15, 17, 18, 21, 23, 25, 29, 30, 35, 37, 39, 42, 43, 45, 47, 53, 55, 60, 65, 67, 69, 72, 73, 77, 81, 83, 85, 95, 99, 102, 103, 105, 107, 108, 111, 113, 125, 127, 129, 131, 133, 137, 138, 143, 145, 149, 150, 151, 155, 157, 161, 163, 165, 173, 175, 180, 185, 187

Offset: 1

Derek Orr, Aug 12 2014

nonn

Subsequence of the complement of (A239321 union A125163).

			5 + 2! = 7 and 5 - 2! = 3 are both prime. Thus 5 is a member of this sequence.

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

Cf. A239321, A125163, A241425, A245716.

a(n)=for(k=1,n,if(ispseudoprime(n+k!)&&ispseudoprime(n-k!),return(k)))
n=1;while(n<500,if(a(n),print1(n,", "));n++)

cp's OEIS Frontend

A241425 Largest number k > 0 such that n + k! and n - k! are both prime, or 0 if no such k exists.

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