Search: id:A143350
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%I A143350
%S A143350 2,4,1,7,1,1,10,2,1,0,15,2,1,0,1,18,3,2,0,1,1,23,3,2,0,1,1,1,26,4,2,0,
               1,
%T A143350 1,1,0,31,4,3,0,1,1,1,0,0,38,5,3,0,2,1,1,0,0,1,41,5,3,0,2,1,1,0,0,1,1,
%U A143350 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
%V A143350 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,-1,
               1,-1,26,-4,-2,0,
%W A143350 -1,1,-1,0,31,-4,-3,0,-1,1,-1,0,0,38,-5,-3,0,-2,1,-1,0,0,1,41,-5,-3,0,
               -2,1,-1,0,0,1,-1,
%X A143350 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 A143350 Triangle read by rows, replace column 1 of triangle A143349 with A095116, 
               1<=k<=n.
%C A143350 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 A143350 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 A143350 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 A143350 First few rows of the triangle =
%e A143350 2;
%e A143350 4, -1;
%e A143350 7, -1, -1;
%e A143350 10, -2, -1, 0;
%e A143350 15, -2, -1, 0, -1;
%e A143350 18, -3, -2, 0, -1, 1;
%e A143350 23, -3, -2, 0, -1, 1, -1;
%e A143350 26, -4, -2, 0, -1, 1, -1, 0;
%e A143350 31, -4, -3, 0, -1, 1, -1, 0, 0;
%e A143350 38, -5, -3, 0, -2, 1, -1, 0, 0, 1;
%e A143350 ...
%Y A143350 Cf. A143349, A095116, A008683, A000040.
%Y A143350 Sequence in context: A137478 A089087 A142146 this_sequence A119303 A105552 
               A112852
%Y A143350 Adjacent sequences: A143347 A143348 A143349 this_sequence A143351 A143352 
               A143353
%K A143350 tabl,sign
%O A143350 1,1
%A A143350 Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 10 2008

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