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%I #2 Mar 30 2012 17:25:31
%S 2,4,-1,7,-1,-1,10,-2,-1,0,15,-2,-1,0,-1,18,-3,-2,0,-1,1,23,-3,-2,0,
%T -1,1,-1,26,-4,-2,0,-1,1,-1,0,31,-4,-3,0,-1,1,-1,0,0,38,-5,-3,0,-2,1,
%U -1,0,0,1,41,-5,-3,0,-2,1,-1,0,0,1,-1,48,-6,-4,0,-2,2,-1,0,0,1,-1,0,53,-6,-4,0,-2,2,-1,0,0,1,-1,0,-1,56,-7,-4,0,-2,2,-2,0,0
%N Triangle read by rows, replace column 1 of triangle A143349 with A095116, 1<=k<=n.
%C Triangle A143349 = a type of Mobius transform which converts sequences to triangles with row sums = the same sequence. In this case, we convert p(n) to triangle A143349 having row sums = p(n), the primes.
%C We begin with p(n), adding (n-1) = A095116: (2, 4, 7, 10, 15, 18, 23,...). We then replace column 1 of triangle A143349 with A095116 resulting in A143350 with row sums = p(n).
%F Triangle read by rows, replace column 1 of triangle A143349 with A095116, 1<=k<=n. A143349 = p(n)+(n-1) & A143349 = a type of Mobius transform.
%e First few rows of the triangle =
%e 2;
%e 4, -1;
%e 7, -1, -1;
%e 10, -2, -1, 0;
%e 15, -2, -1, 0, -1;
%e 18, -3, -2, 0, -1, 1;
%e 23, -3, -2, 0, -1, 1, -1;
%e 26, -4, -2, 0, -1, 1, -1, 0;
%e 31, -4, -3, 0, -1, 1, -1, 0, 0;
%e 38, -5, -3, 0, -2, 1, -1, 0, 0, 1;
%e ...
%Y Cf. A143349, A095116, A008683, A000040.
%K tabl,sign
%O 1,1
%A _Gary W. Adamson_, Aug 10 2008
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