A087377 Triangle read by rows: n-th row contains n smallest numbers k (say) such that nk+1 is a prime.

1, 1, 2, 2, 4, 6, 1, 3, 4, 7, 2, 6, 8, 12, 14, 1, 2, 3, 5, 6, 7, 4, 6, 10, 16, 18, 28, 30, 2, 5, 9, 11, 12, 14, 17, 24, 2, 4, 8, 12, 14, 18, 20, 22, 30, 1, 3, 4, 6, 7, 10, 13, 15, 18, 19, 2, 6, 8, 18, 30, 32, 36, 38, 42, 56, 60, 1, 3, 5, 6, 8, 9, 13, 15, 16, 19, 20, 23, 4, 6, 10, 12, 24, 34

Offset

1,3

Comments

From Robert Israel, May 22 2015: (Start)

If n is odd, all elements in row n are even.

By Dirichlet's theorem, every positive integer occurs infinitely often in the sequence. (End)

Links

Ivan Neretin, Table of n, a(n) for n = 1..5050

Example

1
1 2
2 4 6
1 3 4 7
2 6 8 12 14
1 2 3 5 6 7
4 6 10 16 18 28 30

Maple

F:= proc(n) local res, count, k;
   res:= NULL:
   count:= 0:
   for k from 1 while count < n do
      if isprime(n*k+1) then
        res:= res, k;
        count:= count+1
      fi
   od;
   res
end proc:
seq(F(n), n=1..20); # Robert Israel, May 22 2015

Mathematica

a = {}; Do[k = 0; ar = {}; While[Length[ar] < n, k++; If[PrimeQ[k n + 1], AppendTo[ar, k]]]; a = Join[a, ar], {n, 13}]; a (* Ivan Neretin, May 22 2015 *)

Prog

(PARI) tabl(nn) = {for (n = 1, nn, j = 0; for (k = 1, n, j++; while (!isprime(n*j+1), j++); print1(j, ", "); ); print(); ); } \\ Michel Marcus, May 23 2015

Crossrefs

The first column is given by A034693.

Cf. A034693, A087376.

Sequence in context: A158649 A357886 A019964 * A010768 A143267 A113463

Adjacent sequences: A087374 A087375 A087376 * A087378 A087379 A087380

Keyword

nonn,tabl

Author

Amarnath Murthy, Sep 09 2003

Extensions

More terms from Sam Alexander, Feb 27 2004

Status

approved