A204137 Triangle T(r+1,c) = |T(r,c) - T(r,c+1)| of positive integers such that T(r,c) is prime iff r=1 and no number occurs twice.

2, 3, 1, 13, 10, 9, 47, 34, 24, 15, 197, 150, 116, 92, 77, 11, 186, 36, 80, 12, 65, 29, 18, 168, 132, 52, 40, 25, 443, 414, 396, 228, 96, 44, 4, 21, 397, 46, 368, 28, 200, 104, 60, 56, 35, 1321, 924, 878, 510, 482, 282, 178, 118, 62, 27, 4831, 3510, 2586

Offset

1,1

Comments

For each n>0, T(1,n) = A203985(n) is the smallest prime such that the constraints are satisfied for r+c <= n+1.

It is conjectured that the first row of the table is a permutation of the primes and the whole table, i.e., this sequence, a permutation of the positive integers.

Links

Table of n, a(n) for n=1..58.

Eric Angelini, An array of naturals, Jan 07 2012

Eric Angelini, An array of naturals [Cached copy, with permission]

Example

The triangle starts
r=1:  2 3  13  47 ...   <- primes
r=2:   1 10  34 ...
r=3:    9  24 ...
r=4:     15 ...
which is the smallest solution as can be seen from the fact that the first column contains so far the smallest odd nonprimes. This does not remain true for subsequent rows; the triangle is determined by imposing minimality of the elements of the first row.
See the link for more data.

Prog

(PARI) table_by_antidiagonals(a)={my(u=[]); for(i=1, #a, u=concat(u, a[i]); forstep(j=i-1, 1, -1, u=concat(u, a[j]=abs(a[j]-a[j+1])))); u}
A204137=table_by_antidiagonals( A203985 ) \\  M. F. Hasler, Jan 11 2012

Crossrefs

Cf. A203985.

Sequence in context: A176701 A107415 A079174 * A102583 A030780 A193683

Adjacent sequences: A204134 A204135 A204136 * A204138 A204139 A204140

Keyword

nonn,tabl

Author

Eric Angelini, Jan 07 2012

Extensions

Computed up to a(70*71/2) by Jean-Marc Falcoz, Jan 09 2012

Status

approved