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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 (list; table; graph; refs; listen; history; text; internal format)
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
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
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

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Last modified May 30 04:46 EDT 2024. Contains 372958 sequences. (Running on oeis4.)