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A193471 Square array A(n,k) (n>=1, k>=0) read by antidiagonals: A(n,0) = 0 and A(n,k) is the least integer > A(n,k-1) that can be expressed as a sum of the first prime numbers divided by n.

%I A193471 #14 Mar 03 2014 04:25:30
%S A193471 0,0,2,0,1,5,0,43,5,10,0,7,127,14,17,0,1,25,167,29,28,0,1145,2,40,213,
%T A193471 50,41,0,4,3758,20,82,321,80,58,0,20,11,3932,32,110,387,119,77,0,71,
%U A193471 41,34,4300,88,142,457,164,100,0,1,107,55,113,4490,212,178,531,220,129,0,7,10
%N A193471 Square array A(n,k) (n>=1, k>=0) read by antidiagonals: A(n,0) = 0 and A(n,k) is the least integer > A(n,k-1) that can be expressed as a sum of the first prime numbers divided by n.
%H A193471 Vincenzo Librandi, <a href="/A193471/b193471.txt">Table of n, a(n) for n = 1..1275</a>
%e A193471 n\k  0   1   2    3    4     5     6    7
%e A193471 -----------------------------------------
%e A193471 1 |  0    2    5   10   17   28   41   58  A007504
%e A193471 2 |  0    1    5   14   29   50   80  119
%e A193471 3 |  0   43  127  167  213  321  387  457  A112270
%e A193471 4 |  0    7   25   40   82  110  142  178
%e A193471 5 |  0    1    2   20   32   88  212  296  A112271
%e A193471 6 |  0 1145 3758 3932 4300 4490 4684 5084
%e A193471 7 |  0    4   11   34  113  284  441  634  A112272
%e A193471 8 |  0   20   41   55   71   89  158  185
%p A193471 A193471_rect := proc(n,k) local j, i, L; L := NULL; j := 0;
%p A193471 while nops([L]) < k do add(ithprime(i)/n, i=1..j);
%p A193471 if type(%,integer) then L := L,% fi; j := j+1 od; L end:
%p A193471 seq(print(A193471_rect(n, 8)), n = 1..8);
%t A193471 max = 12; rect[n_, k_] := Module[{j, i, L, s}, L = {}; j = 0; While[Length[L]<k, s = Sum[Prime[i]/n, {i, 1, j}]; If[IntegerQ[s], AppendTo[L, s]]; j = j+1]; L]; a[_, 0] = 0; a[n_, k_] := rect[n, max][[k+1]]; Table[a[n-k, k], {n, 1, max} , {k, 0, n-1}] // Flatten (* _Jean-François Alcover_, Feb 25 2014, after Maple *)
%Y A193471 Cf. A193470.
%K A193471 nonn,tabl
%O A193471 1,3
%A A193471 _Peter Luschny_, Jul 29 2011