A079022 - OEIS

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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

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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