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A079022
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Suppose p and q = p+2n are primes. Define the difference pattern of (p,q) to be the successive differences of the primes in the range p to q. There are a(n) possible difference patterns.
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1
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1, 2, 3, 5, 5, 14, 15, 17, 49, 56, 51, 175, 150
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| n=4, d=8: there are five difference patterns: [8], [6,2], [2,6], [2,4,2], [2,2,4]. The last pattern is singular with prime 4-tuple {p=3,5,7,11=q}.
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MATHEMATICA
| t[x_] := Table[Length[FactorInteger[x+j]], {j, 0, d}] p[x_] := Flatten[Position[Table[PrimeQ[x+2*j], {j, 0, d/2}], True]] dp[x_] := Delete[RotateLeft[p[x]]-p[x], -1] k=0; d=30; {n1=2, n2=35000000} {h0=PrimePi[n1], h=PrimePi[n2]; t1={}; Do[s=Prime[n]; If[PrimeQ[s + d], k=k+1; Print[{k, s, pt=2*dp[s]}]; t1=Union[t1, {2*dp[s]}], 1], {n, h0, h}] t1 {d, n1, n2, k, Length[t1]} (program for d=30; partition list is enlargable if t1={} is replaced with already obtained set)
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CROSSREFS
| See A079016-A079021 for illustrations of the cases n=6 through 11.
Cf. A000230, A079016-A079024.
Sequence in context: A097453 A079125 A146305 * A095296 A157260 A177870
Adjacent sequences: A079019 A079020 A079021 * A079023 A079024 A079025
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jan 24 2003
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