A119446 Triangle as described in A100461, except with t(1,n) = prime(n).

2, 2, 3, 3, 4, 5, 3, 4, 6, 7, 3, 4, 6, 8, 11, 3, 4, 6, 8, 10, 13, 3, 4, 6, 8, 10, 12, 17, 3, 4, 6, 8, 10, 12, 14, 19, 3, 4, 6, 8, 10, 12, 14, 16, 23, 7, 8, 9, 12, 15, 18, 21, 24, 27, 29, 7, 8, 9, 12, 15, 18, 21, 24, 27, 30, 31, 7, 8, 9, 12, 15, 18, 21, 24, 27, 30, 33, 37

Offset: 1

Author

Joshua Zucker, May 20 2006

Keywords

• nonn
• tabl

Examples

			Triangle begins as:
  2;
  2, 3;
  3, 4, 5;
  3, 4, 6,  7;
  3, 4, 6,  8, 11;
  3, 4, 6,  8, 10, 13;
  3, 4, 6,  8, 10, 12, 17;
  3, 4, 6,  8, 10, 12, 14, 19;
  3, 4, 6,  8, 10, 12, 14, 16, 23;
  7, 8, 9, 12, 15, 18, 21, 24, 27, 29;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A100461 for powers of 2, A119444 for Fibonacci and A119447 for leading diag. of this triangle.

Programs

Magma

function t(n,k) // t = A119444
  if k eq 1 then return NthPrime(n);
  else return (n-k+1)*Floor((t(n,k-1) -1)/(n-k+1));
  end if;
end function;
[t(n,n-n+1): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 07 2023

Mathematica

t[n_, k_]:= t[n, k]= If[k==1, Prime[n], (n-k+1)*Floor[(t[n,k-1] -1)/(n -k+1)]];
Table[t[n, n-k+1], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Apr 07 2023 *)

SageMath

def t(n, k):
    if (k==1): return nth_prime(n)
    else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
flatten([[t(n, n-k+1) for k in range(1,n+1)] for n in range(1, 16)]) # G. C. Greubel, Apr 07 2023

Formula

Form an array t(m,n) (n >= 1, 1 <= m <= n) by: t(1,n) = prime(n) for all n; t(m+1,n) = (n-m)*floor( (t(m,n) - 1)/(n-m) ) for 1 <= m <= n-1.