This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A079022 #29 Feb 18 2021 00:49:27
%S A079022 1,2,3,5,5,14,15,17,49,56,51,175,150,148,666,581,561,1922,1449
%N 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.
%e A079022 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}.
%t A079022 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 *)
%Y A079022 See A079016, A079017, A079018, A079019, A079020, A079021 for cases n=6 through 11.
%Y A079022 Cf. A000230, A079023, A079024.
%K A079022 nonn,more
%O A079022 1,2
%A A079022 _Labos Elemer_, Jan 24 2003
%E A079022 a(14)-a(17) and a(19) from _David A. Corneth_, Aug 30 2019
%E A079022 a(18) from _Jinyuan Wang_, Feb 16 2021