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.

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, 50, 41, 0, 4, 3758, 20, 82, 321, 80, 58, 0, 20, 11, 3932, 32, 110, 387, 119, 77, 0, 71, 41, 34, 4300, 88, 142, 457, 164, 100, 0, 1, 107, 55, 113, 4490, 212, 178, 531, 220, 129, 0, 7, 10

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1275

Example

n\k  0   1   2    3    4     5     6    7
-----------------------------------------
1 |  0    2    5   10   17   28   41   58  A007504
2 |  0    1    5   14   29   50   80  119
3 |  0   43  127  167  213  321  387  457  A112270
4 |  0    7   25   40   82  110  142  178
5 |  0    1    2   20   32   88  212  296  A112271
6 |  0 1145 3758 3932 4300 4490 4684 5084
7 |  0    4   11   34  113  284  441  634  A112272
8 |  0   20   41   55   71   89  158  185

Maple

A193471_rect := proc(n, k) local j, i, L; L := NULL; j := 0;
while nops([L]) < k do add(ithprime(i)/n, i=1..j);
if type(%, integer) then L := L, % fi; j := j+1 od; L end:
seq(print(A193471_rect(n, 8)), n = 1..8);

Mathematica

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 *)

Crossrefs

Cf. A193470.

Sequence in context: A321619 A285212 A262948 * A351645 A182931 A260615

Adjacent sequences: A193468 A193469 A193470 * A193472 A193473 A193474

Keyword

nonn,tabl

Author

Peter Luschny, Jul 29 2011

Status

approved