|
| |
|
|
A143350
|
|
Triangle read by rows, replace column 1 of triangle A143349 with A095116, 1<=k<=n.
|
|
3
| |
|
|
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
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
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).
|
|
|
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 * A119303 A105552 A112852
Adjacent sequences: A143347 A143348 A143349 * A143351 A143352 A143353
|
|
|
KEYWORD
| tabl,sign
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 10 2008
|
| |
|
|
