login
A087907
Numbers n such that n*359# +-1 are twin primes, where 359# = 72nd primorial (A002110(72)).
0
983, 1211, 1345, 2134, 2260, 4981, 8102, 9788, 10074, 10406, 10923, 11254, 11821, 11896, 12122, 14428, 14809, 15568, 15758, 17909, 23197, 24634, 25646, 26236, 26781, 27850, 28648, 30739, 31515, 31671, 37875, 40653, 41621, 43983, 44773
OFFSET
1,1
COMMENTS
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
For i=72, P(i)=359, 115 j values, int(16*log(2*359))=105
For i=26, P(i)=101, 67 j values, int(16*log(2*101))=73
For i=38, P(i)=163, 107 j values, int(16*log(2*163))=81
For i=50, P(i)=229, 102 j values, int(16*log(2*229))=98
EXAMPLE
134464*359# -1 and +1 are twin primes, 134464 is the 115th j value and the last of this sequence
MATHEMATICA
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 *)
CROSSREFS
P# = A002110.
Sequence in context: A251839 A122472 A252402 * A351665 A182574 A096701
KEYWORD
nonn
AUTHOR
Pierre CAMI, Oct 15 2003
EXTENSIONS
Needs to be edited in a similar manner to A087820. - N. J. A. Sloane
STATUS
approved