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.

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

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

Alois P. Heinz, Rows n = 1..200, flattened

E. Angelini, Vertices, edges, primes and non-primes, SeqFan list, Sept. 16, 2015.

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

Cf. A261298: main diagonal T(n,n).

Cf. A000040: primes, A018252: nonprimes.

Column k=1 gives A261211.

Sequence in context: A093049 A326146 A081243 * A308034 A289918 A127480

Adjacent sequences: A261294 A261295 A261296 * A261298 A261299 A261300

Keyword

nonn,tabl,look

Author

M. F. Hasler, Sep 16 2015

Status

approved