A082196 Triangle read by rows in which the n-th row contains n distinct numbers (not occurring earlier) such that every entry is coprime to its neighbor in all directions.

1, 2, 3, 5, 7, 4, 6, 11, 9, 13, 17, 19, 8, 23, 10, 12, 25, 21, 29, 27, 31, 37, 41, 16, 43, 14, 47, 15, 18, 35, 33, 53, 39, 59, 22, 49, 61, 67, 26, 71, 20, 73, 45, 79, 24, 28, 51, 55, 57, 77, 83, 32, 89, 65, 97, 95, 101, 46, 103, 34, 69, 85, 63, 38, 81, 40, 36, 91, 75, 107, 109, 113, 44, 127, 115, 119, 121, 87

Offset

1,2

Links

Alois P. Heinz, Rows n = 1..141, flattened

Example

Triangle begins
   1;
   2,  3;
   5,  7,  4;
   6, 11,  9, 13;
  17, 19,  8, 23, 10;
  ...
a(4,2) = 11. Its 8 neighbors are 5,7,4,9,8,19,17 and 6, which are coprime to 11.

Maple

ina:= proc() false end: mina:= 2:
T:= proc(n, k) option remember; global mina; local t;
      if n<2 or k<1 or k>n then 1
    else for t from mina while ina(t) or [1$4] <> map (x->igcd(x, t),
            [T(n-1, k-1), T(n-1, k), T(n-1, k+1), T(n, k-1)])
         do od; ina(t):= true;
         while ina(mina) do mina:= mina+1 od;
         t
      fi
    end:
seq (seq (T(n, k), k=1..n), n=1..15);  # Alois P. Heinz, Sep 10 2011

Mathematica

ina[_] = False; mina = 2; T[n_, k_] := T[n, k] = If[n<2 || k<1 || k>n, 1, For[t = mina, ina[t] || Array[1&, 4] != Map [GCD[#, t]&, List[T[n-1, k-1], T[n-1, k], T[n-1, k+1], T[n, k-1]]], t++]; ina[t] = True; While[ina[mina], mina = mina+1]; t]; Table[Table[T[n, k], {k, 1, n}], {n, 1, 15}] // Flatten (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *)

Crossrefs

Cf. A082197, A082198, A082199.

Sequence in context: A290020 A178595 A098284 * A292876 A126049 A291603

Adjacent sequences: A082193 A082194 A082195 * A082197 A082198 A082199

Keyword

nonn,tabl

Author

Amarnath Murthy, Apr 07 2003

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003

Status

approved