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A174873 Difference d between two distinct primes a and b such that a*b+-d are primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A077121 A302488 A140495 * A213172 A280984 A008810

Adjacent sequences:  A174870 A174871 A174872 * A174874 A174875 A174876

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Mar 31 2010

STATUS

approved

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Last modified December 6 09:36 EST 2019. Contains 329794 sequences. (Running on oeis4.)