A087907 - OEIS

%I #11 Oct 29 2017 16:01:38

%S 983,1211,1345,2134,2260,4981,8102,9788,10074,10406,10923,11254,11821,

%T 11896,12122,14428,14809,15568,15758,17909,23197,24634,25646,26236,

%U 26781,27850,28648,30739,31515,31671,37875,40653,41621,43983,44773

%N Numbers n such that n*359# +-1 are twin primes, where 359# = 72nd primorial (A002110(72)).

%C For the i-th primorial there are roughly floor(16*log(2*P(i))) solutions j for the Diophantine equation: j*P(i)# -1 and +1 are prime twins with i >= 7

%C For i=72, P(i)=359, 115 j values, int(16*log(2*359))=105

%C For i=26, P(i)=101, 67 j values, int(16*log(2*101))=73

%C For i=38, P(i)=163, 107 j values, int(16*log(2*163))=81

%C For i=50, P(i)=229, 102 j values, int(16*log(2*229))=98

%e 134464*359# -1 and +1 are twin primes, 134464 is the 115th j value and the last of this sequence

%t With[{pmrl=Fold[Times,Prime[Range[72]]]},Select[Range[45000],AllTrue[ pmrl*#+{1,-1},PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Oct 29 2017 *)

%Y P# = A002110.

%K nonn

%O 1,1

%A _Pierre CAMI_, Oct 15 2003

%E Needs to be edited in a similar manner to A087820. - _N. J. A. Sloane_