1,4

Diagonal[{p(i)-p(i)}] of difference-matrices is to neglect since consisting of zeros.

The complete diversity of k-1 consecutive prime differences [as in A079007] is a necessary but not sufficient condition for providing C[k,2] distinct entries in the corresponding k X k difference-matrix of k consecutive primes. Consecutive prime differences are para-diagonal entries in the difference-matrix. So conditions here are stronger than in A079007.

Subscripts at which sequences like A098726, A098206-A098212 reach first their possible maximum, i.e. C[k, 2] with the corresponding k.

At n=1, 2, 3, the maxima are C[n, 2]=0, 1, 3 reached at a[n]=1, 1, 1 respectively;

n=7:a[7]=374, primes={p(374),..,p(80)}= {2551,2557,2579,2591,2593,2609,2617}.Building Abs[p(i)-p(j)] 7x7-matrix, the number of its distinct positive entries equals C[7,2]=21, namely:{2,6,8,12,14,16,18,22,24,26,28,30,34,36,38,40,42,52,58,60,66};

n=12: a(12)=2332720, list of 12 primes = {p(n),..,p(n+11)} ={38238461,..,38238737}; 12x12-matrix={abs[(p()-p(j)]}, number of distinct entries=C[12,2]=66, that of {2,6,8,.....,266,274,276}.

Cf. A098726, A098206-A098216, A080370.

Sequence in context: A126858 A113751 A107233 this_sequence A163613 A050477 A055737

Adjacent sequences: A098210 A098211 A098212 this_sequence A098214 A098215 A098216

nonn

Labos E. (labos(AT)ana.sote.hu), Oct 05 2004