A139188 Greater twin prime member A006512 of the form k!/n + 1.

7, 13, 241, 7, 7983361, 5

Offset: 1

Author

Artur Jasinski, Apr 11 2008

Keywords

• nonn
• more

Comments

Given n, the sequence shows the smallest A006512(j) = a(n) of the form k!/n - 1.

The associated lower twin prime is A139187(n) = A001359(j) = a(n) - 2,

and the associated factorial index is k(n) = A139186(n).

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, 453601, 0, 13, 0, 61, 0, 0, 2689, 0, 0, 0, 2688996956405760001, 7, 241, 0, 0, 31, 44960029111104307201, 0, 134401, 181, 0, 5, 0, 0, 0, 0, 1153, 100801, 0, 0, 536481792001, 19, 0, 0, 0, 141523201, 0, 1313375283986387731246850697141608641462272000000001, 0, 7561, 0, 8065829222532112711680001. - Hugo Pfoertner, Mar 30 2020

Crossrefs

Cf. A139186, A139187.

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

Formula

a(n) = A139187(n)+2 = A000142(A139186(n))/n+1 .