

A261297


Triangle read by rows, where row n contains the n smallest available numbers of primality opposite to that of n, subject to the restriction that in the whole triangle each number k can be used only k times.


3



2, 1, 4, 4, 6, 8, 2, 3, 5, 7, 4, 6, 8, 9, 10, 3, 5, 7, 11, 13, 17, 4, 6, 8, 9, 10, 12, 14, 3, 5, 7, 11, 13, 17, 19, 23, 5, 7, 11, 13, 17, 19, 23, 29, 31, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67
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OFFSET

1,1


COMMENTS

If n is prime the entries in row n must be nonprimes, and vice versa.
The sequence can be interpreted as a graph, see Eric Angelini's post to the SeqFan list.


LINKS



EXAMPLE

The table starts:
row: data T(n,k); k=1..n
1: [2]
2: [1, 4]
3: [4, 6, 8]
4: [2, 3, 5, 7]
5: [4, 6, 8, 9, 10]
6: [3, 5, 7, 11, 13, 17]
7: [4, 6, 8, 9, 10, 12, 14]
8: [3, 5, 7, 11, 13, 17, 19, 23]
9: [5, 7, 11, 13, 17, 19, 23, 29, 31]
10: [5, 7, 11, 13, 17, 19, 23, 29, 31, 37]
11: [6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21]
12: [7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
13: [6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24]
14: [7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59]


PROG

(PARI) {c=[[1, 0]]; for(n=1, 20, while(#c>1 && c[1][1]==c[1][2], c=c[2..1]); r=[]; j=0; while(#r<n, j++>#c && c=concat(c, [[c[#c][1]+1, 0]]); isprime(n)!=isprime(c[j][1]) && c[j][2]<c[j][1] && c[j][2]++ && r=concat(r, c[j][1])); print(r))}


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



