A139186 a(n) is the smallest k such that k!/n +- 1 is a twin prime pair.

3, 4, 6, 4, 11, 4

Offset

1,1

Comments

Smallest factorial indices k such that (k!/n-1, k!/n+1) = (A001359(j), A006512(j)) for some twin prime index j.

If it exists, a(7) > 1000. A continuation of the sequence, with unknown terms indicated by 0, is a(8)..a(50): 10, 0, 5, 0, 6, 0, 0, 8, 0, 0, 0, 21, 5, 7, 0, 0, 6, 22, 0, 10, 7, 0, 5, 0, 0, 0, 0, 8, 10, 0, 0, 16, 6, 0, 0, 0, 13, 0, 43, 0, 9, 0, 26. The unknown terms have been checked through k <= 1000. - Hugo Pfoertner, Mar 29 2020

Links

Table of n, a(n) for n=1..6.

Formula

A000142(a(n))/n - 1 = A139187(n).

A000142(a(n))/n + 1 = A139188(n).

Example

For n=6, solutions to k!/n - 1 = A001359(j) are given by k = 4, 11, 13, 17, ...
The smallest k out of these, k=4, is a(6).

Mathematica

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

Prog

(PARI) a(n) = {my(k=1); while (! ((denominator(m=k!/n)==1) && isprime(m-1) && isprime(m+1)), k++); k; } \\ Michel Marcus, Mar 29 2020

Crossrefs

Cf. A139187, A139188.

Sequence in context: A238502 A023823 A279081 * A326417 A047840 A037189

Adjacent sequences: A139183 A139184 A139185 * A139187 A139188 A139189

Keyword

nonn,more

Author

Artur Jasinski, Apr 11 2008

Status

approved