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Least multiple of n! sandwiched between twin primes, or 0 if no such number exists.
2

%I #13 Jan 27 2020 13:40:40

%S 4,4,6,72,240,12240,35280,241920,1088640,50803200,1157587200,

%T 14370048000,298896998400,2353813862400,11769069312000,

%U 502146957312000,4268249137152000,621030249455616000,9488317831888896000

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

%C Conjecture: No term is zero.

%C This conjecture is implied by Dickson's conjecture. - _Robert Israel_, Feb 13 2018

%H Robert Israel, <a href="/A090531/b090531.txt">Table of n, a(n) for n = 1..447</a>

%F a(n) = A071256(A000142(n)). - _Robert Israel_, Feb 13 2018

%p 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;

%p map(f, [`$`(1 .. 20)]); # _Robert Israel_, Feb 13 2018

%t 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 *)

%Y Cf. A000142, A071256, A090530.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Dec 07 2003

%E More terms from _Ryan Propper_, Jun 16 2005