1,1

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.

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).

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.

First few rows of the triangle =

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, 1, -1, 0;

31, -4, -3, 0, -1, 1, -1, 0, 0;

38, -5, -3, 0, -2, 1, -1, 0, 0, 1;

...

Cf. A143349, A095116, A008683, A000040.

Sequence in context: A137478 A089087 A142146 this_sequence A119303 A105552 A112852

Adjacent sequences: A143347 A143348 A143349 this_sequence A143351 A143352 A143353

tabl,sign

Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 10 2008