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A098214 Sequence of special consecutive prime differences which can be arranged into rows of distinct differences with k=1,2,3,...length. Each row is obtained from segment of k+1 consecutive primes started with A079007[k]. 0

%I #4 Oct 15 2013 22:32:34

%S 1,1,2,2,4,6,6,8,4,2,14,4,6,2,10,8,4,6,12,2,18,6,8,18,10,14,4,2,10,12,

%T 8,16,14,6,4,2,10,2,16,6,20,4,12,14,28,4,14,22,12,2,18,10,6,26,24,14,

%U 16,6,20,10,12,2,18,42,4,24,18,6,4,20,22,8,12,24,16,14,10,30,6,4,20,22,8,12

%N Sequence of special consecutive prime differences which can be arranged into rows of distinct differences with k=1,2,3,...length. Each row is obtained from segment of k+1 consecutive primes started with A079007[k].

%C Rows generated by n-th term of A079007 are all distinct. See definition of A079007.

%e Triangle begins:

%e 1,

%e 1,2,

%e 2,4,6,

%e 6,8,4,2,

%e 14,4,6,2,10,

%e 8,4,6,12,2,18,

%e 6,8,18,10,14,4,2,

%e 10,12,8,16,14,6,4,2,

%e 10,2,16,6,20,4,12,14,28,

%e 4,14,22,12,2,18,10,6,26,24,

%e 14,16,6,20,10,12,2,18,42,4,24,

%e 18,6,4,20,22,8,12,24,16,14,10,30,

%e 6,4,20,22,8,12,24,16,14,10,30,18,2,

%e 16,8,22,26,4,24,20,6,58,12,14,10,36,18,

%e 16,8,22,26,4,24,20,6,58,12,14,10,36,18,2,

%e The 6th row {8,4,6,12,2,18}={a[16],...a[21]} is obtained as first

%e difference sequence of 7 primes started with prime[94]=491=A079007[6].

%e The k-th row starts and ends with terms a[1+k(k-1)/2] and a[ -1+k+k(k-1)/2].

%Y Cf. A001223, A079007, A098213.

%K nonn,tabl

%O 1,3

%A _Labos Elemer_, Oct 21 2004

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