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

%I A119446 #6 Apr 07 2023 17:16:14
%S A119446 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,
%T A119446 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,
%U A119446 9,12,15,18,21,24,27,30,31,7,8,9,12,15,18,21,24,27,30,33,37
%N A119446 Triangle as described in A100461, except with t(1,n) = prime(n).
%H A119446 G. C. Greubel, <a href="/A119446/b119446.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A119446 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.
%e A119446 Triangle begins as:
%e A119446   2;
%e A119446   2, 3;
%e A119446   3, 4, 5;
%e A119446   3, 4, 6,  7;
%e A119446   3, 4, 6,  8, 11;
%e A119446   3, 4, 6,  8, 10, 13;
%e A119446   3, 4, 6,  8, 10, 12, 17;
%e A119446   3, 4, 6,  8, 10, 12, 14, 19;
%e A119446   3, 4, 6,  8, 10, 12, 14, 16, 23;
%e A119446   7, 8, 9, 12, 15, 18, 21, 24, 27, 29;
%t A119446 t[n_, k_]:= t[n, k]= If[k==1, Prime[n], (n-k+1)*Floor[(t[n,k-1] -1)/(n -k+1)]];
%t A119446 Table[t[n, n-k+1], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Apr 07 2023 *)
%o A119446 (Magma)
%o A119446 function t(n,k) // t = A119444
%o A119446   if k eq 1 then return NthPrime(n);
%o A119446   else return (n-k+1)*Floor((t(n,k-1) -1)/(n-k+1));
%o A119446   end if;
%o A119446 end function;
%o A119446 [t(n,n-n+1): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Apr 07 2023
%o A119446 (SageMath)
%o A119446 def t(n, k):
%o A119446     if (k==1): return nth_prime(n)
%o A119446     else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
%o A119446 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
%Y A119446 Cf. A100461 for powers of 2, A119444 for Fibonacci and A119447 for leading diag. of this triangle.
%K A119446 nonn,tabl
%O A119446 1,1
%A A119446 _Joshua Zucker_, May 20 2006