A139187 Smallest twin prime member A001359 of the form k!/n-1.

5, 11, 239, 5, 7983359, 3

Offset: 1

Author

Artur Jasinski, Apr 11 2008

Keywords

• nonn
• more

Comments

"Factorial" twin primes are a pair (k!/n-1, k!/n+1) = (A001359(j), A006512(j)).

Given n, the sequence shows the smallest a(n)=A001359(j) solving this pair equation.

The associated upper twin prime is A139188(n) = A006512(j) = A001359(j)+2 = a(n)+2, and the associated factorial index is k(n) = A139186(n).

The twin prime indices j(n) are 2, 3, 17, 2, 48525, 1.

a(7) is unknown, with k(7) > 25000. A continuation of the sequence, with unknown terms indicated by 0, is a(7)..a(50): 0, 453599, 0, 11, 0, 59, 0, 0, 2687, 0, 0, 0, 2688996956405759999, 5, 239, 0, 0, 29, 44960029111104307199, 0, 134399, 179, 0, 3, 0, 0, 0, 0, 1151, 100799, 0, 0, 536481791999, 17, 0, 0, 0, 141523199, 0, 1313375283986387731246850697141608641462271999999999, 0, 7559, 0, 8065829222532112711679999. - Hugo Pfoertner, Mar 30 2020

Examples

			For n=1, the smallest k is 3, where (3!/1-1,3!/1+1) = (5,7) = (A001359(2),A006512(2)).
For n=3, the smallest k is 6, where (6!/3-1,6!/3+1) = (239,241) = (A001359(17),A006512(17)).
		

Crossrefs

Cf. A139186, A139188.

Programs

Mathematica

a = {}; Do[k = 1; While[ ! (PrimeQ[(k! - n)/n] && PrimeQ[(k! + n)/n]), k++ ]; AppendTo[a, (k! - n)/n], {n, 1, 6}]; a