A079022 Suppose p and q = p + 2*n 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.

1, 2, 3, 5, 5, 14, 15, 17, 49, 56, 51, 175, 150, 148, 666, 581, 561, 1922, 1449

Offset

1,2

Links

Table of n, a(n) for n=1..19.

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}.

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=12; {n1=2, n2=2000, 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}]; {d, n1, n2, Length[t1], t1} (* program for d=12; partition list is enlargable if t1={} is replaced with already obtained set *)

Crossrefs

See A079016, A079017, A079018, A079019, A079020, A079021 for cases n=6 through 11.

Cf. A000230, A079023, A079024.

Sequence in context: A079125 A146305 A342437 * A368706 A368674 A095296

Adjacent sequences: A079019 A079020 A079021 * A079023 A079024 A079025

Keyword

nonn,more

Author

Labos Elemer, Jan 24 2003

Extensions

a(14)-a(17) and a(19) from David A. Corneth, Aug 30 2019

a(18) from Jinyuan Wang, Feb 16 2021

Status

approved