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 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 (list; table; graph; refs; listen; history; text; internal format)
 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#c && c=concat(c, [[c[#c][1]+1, 0]]); isprime(n)!=isprime(c[j][1]) && c[j][2]

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Last modified August 10 12:00 EDT 2024. Contains 375056 sequences. (Running on oeis4.)