

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.


1



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
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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.


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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=i1, 1, 1, u=concat(u, a[j]=abs(a[j]a[j+1])))); u}


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AUTHOR



EXTENSIONS



STATUS

approved



