A090531 Least multiple of n! sandwiched between twin primes, or 0 if no such number exists.

4, 4, 6, 72, 240, 12240, 35280, 241920, 1088640, 50803200, 1157587200, 14370048000, 298896998400, 2353813862400, 11769069312000, 502146957312000, 4268249137152000, 621030249455616000, 9488317831888896000

Offset: 1

Author

Amarnath Murthy, Dec 07 2003

Keywords

• nonn

Comments

Conjecture: No term is zero.

This conjecture is implied by Dickson's conjecture. - Robert Israel, Feb 13 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..447

Crossrefs

Cf. A000142, A071256, A090530.

Programs

Maple

f := proc (n) local k, t; t := factorial(n); for k from t by t do if isprime(k-1) and isprime(k+1) then return k end if end do end proc;
map(f, [`$`(1 .. 20)]); # Robert Israel, Feb 13 2018

Mathematica

lmn[n_]:=Module[{k=n!,m=1},While[AnyTrue[k*m+{1,-1},CompositeQ],m++];k*m]; Join[{4,4},Array[lmn,20,3]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 27 2020 *)

Formula

a(n) = A071256(A000142(n)). - Robert Israel, Feb 13 2018

Extensions

More terms from Ryan Propper, Jun 16 2005