A350455 T(n,k) is the k-th semiprime whose sum of prime factors equals 2n, triangle T(n,k), n>=2, 1<=k<=A045917(n), read by rows.

4, 9, 15, 21, 25, 35, 33, 49, 39, 55, 65, 77, 51, 91, 57, 85, 121, 95, 119, 143, 69, 133, 169, 115, 187, 161, 209, 221, 87, 247, 93, 145, 253, 289, 155, 203, 299, 323, 217, 361, 111, 319, 391, 185, 341, 377, 437, 123, 259, 403, 129, 205, 493, 529, 215, 287, 407

Offset

2,1

Comments

Assuming Goldbach's conjecture, no row is empty.

Links

Alois P. Heinz, Rows n = 2..1000, flattened

Wikipedia, Goldbach's conjecture

Example

Triangle T(n,k) begins:
    4;
    9;
   15;
   21,  25;
   35     ;
   33,  49;
   39,  55;
   65,  77;
   51,  91;
   57,  85, 121;
   95, 119, 143;
   69, 133, 169;
  115, 187     ;
  161, 209, 221;
   87, 247     ;
   93, 145, 253, 289;
  155, 203, 299, 323;
  ...

Maple

T:= n-> seq(`if`(andmap(isprime, [h, 2*n-h]), h*(2*n-h), [][]), h=2..n):
seq(T(n), n=2..30);

Crossrefs

Column k=1 gives A073046.

Last elements of rows give A102084.

Row sums give A228553.

Row products give A337568.

Row lengths give A045917.

Cf. A000040, A001358, A046315, A350419.

Sequence in context: A313279 A107986 A062721 * A104243 A313280 A313281

Adjacent sequences: A350452 A350453 A350454 * A350456 A350457 A350458

Keyword

nonn,look,tabf

Author

Alois P. Heinz, Dec 31 2021

Status

approved