A087907 Numbers n such that n*359# +-1 are twin primes, where 359# = 72nd primorial (A002110(72)).

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

Links

Table of n, a(n) for n=1..35.

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

Adjacent sequences: A087904 A087905 A087906 * A087908 A087909 A087910

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