%I #8 Mar 05 2015 07:41:33

%S 3,2,2,11,3,2,3,5,2,3,7,3,7,5,2,7,3,3,5,5,2,5,3,11,3

%N Smallest prime P such that n*P# -1 and n*P# +1 are twin primes, where P#=primorial P, or 0 if no such prime exists.

%C No solutions found yet for n = {26, 39, 46, 59, 63, 68, 76, 81, 82, 84, 89} through prime(1700) = 14519. - _Ray Chandler_, Jan 23 2005

%C The sequence continues: a(26)=?, 5, 7, 7, 2, 19, 3, 3, 5, 5, 2, 19, 3, a(39)=?, 3, 5, 7, 5, 5, 3, a(46)=?, 3, 11, 17, 7, 2, 3, 43, 2, 7, 37, 7, 3, a(59)=?, 151, 31, 13, a(63)=?. - _Robert G. Wilson v_, Jan 12 2005

%e For n=4:

%e 4*2=8 8-1=7 prime but 8+1=9=3*3.

%e 4*2*3=24 24-1=23 prime but 24+1=25=5*5.

%e 4*2*3*5=120 120-1=119=7*17.

%e 4*2*3*5*7=840 840-1=839 prime but 840+1=841=29*29.

%e 4*2*3*5*7*11=9240 9240-1=9239 prime 9240+1=9241 prime so for n=4 P=11.

%t Primorial[n_] := Product[Prime[i], {i, n}]; f[n_] := Block[{k = 1}, While[p = n*Primorial[k]; !PrimeQ[p - 1]\ || ! PrimeQ[p + 1], k++ ]; Prime[k]]; Table[ f[n], {n, 25}] (* _Robert G. Wilson v_, Jan 12 2005 *)

%Y Cf. A060256.

%K nonn,more

%O 1,1

%A _Pierre CAMI_, Jan 04 2005