A174873 Difference d between two distinct primes a and b such that a*b+-d are primes.

1, 2, 3, 6, 9, 12, 16, 18, 24, 26, 30, 36, 42, 48, 54, 60, 66, 69, 72, 78, 84, 86, 90, 96, 102, 108, 110, 114, 120, 126, 132, 135, 138, 144, 150, 156, 162, 168, 174, 180, 186, 189, 190, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 280

Offset

1,2

Comments

2*3=6;3-2=1;6+-1->primes, 3*5=15;5-3=2;15+-2->primes, 2*5=10;5-2=3;10+-3->primes, 7*11=77;11-7=6;77+-6->primes, 22=2*11;11-2=9;22+-9->primes,..

Links

Table of n, a(n) for n=1..59.

Mathematica

lst={}; Do[pa=Prime[a]; Do[pb=Prime[b]; sp=pa*pb; dp=Abs[pa-pb]; If[PrimeQ[sp-dp]&&PrimeQ[sp+dp], AppendTo[lst, dp]], {b, a+1, 3*6!}], {a, 3*6!}]; Take[Union@lst, 120]
d2dQ[{a_, b_}]:=Module[{c=b-a}, AllTrue[a*b+{c, -c}, PrimeQ]]; With[ {nn= 100}, Take[#[[2]]-#[[1]]&/@Select[Union[Sort/@Tuples[ Prime[ Range[ 3nn]], 2]], d2dQ]//Union, nn]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 11 2017 *)

Crossrefs

Cf. A088708.

Sequence in context: A302488 A348448 A140495 * A213172 A008810 A280984

Adjacent sequences: A174870 A174871 A174872 * A174874 A174875 A174876

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 31 2010

Status

approved