A143350 Triangle read by rows, replace column 1 of triangle A143349 with A095116, 1<=k<=n.

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, 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

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..100.

Formula

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.

Example

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;
...

Crossrefs

Cf. A143349, A095116, A008683, A000040.

Sequence in context: A137478 A089087 A142146 * A302541 A119303 A374116

Adjacent sequences: A143347 A143348 A143349 * A143351 A143352 A143353

Keyword

tabl,sign

Author

Gary W. Adamson, Aug 10 2008

Status

approved