A302445 Triangle read by rows: row n gives primes of form k^2 + n - k for 0 < k < n.

2, 3, 5, 5, 7, 11, 17, 7, 13, 19, 37, 11, 29, 11, 13, 17, 23, 31, 41, 53, 67, 83, 101, 13, 19, 43, 103, 17, 71, 197, 17, 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257, 19, 31, 61, 109, 151, 229, 23, 41, 131, 293, 401, 23, 29, 43, 53, 79, 113, 179, 233, 263, 443

Offset

2,1

Links

Seiichi Manyama, Rows n = 2..421, flattened

Eric Weisstein's World of Mathematics, Lucky Number of Euler

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Wikipedia, Lucky numbers of Euler

Example

  n\k|  1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16
  ---+-----------------------------------------------------------------------
    2|  2;
    3|  3,  5;
    4|
    5|  5,  7, 11, 17;
    6|
    7|  7,   , 13, 19,   , 37;
    8|
    9|   , 11,   ,   , 29,   ,   ,   ;
   10|
   11| 11, 13, 17, 23, 31, 41, 53, 67, 83, 101;
   12|
   13| 13,   , 19,   ,   , 43,   ,   ,   , 103,    ,    ;
   14|
   15|   , 17,   ,   ,   ,   ,   , 71,   ,    ,    ,    ,    , 197;
   16|
   17| 17, 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257;

Mathematica

Map[Union@ Select[#, PrimeQ] &, Table[k^2 + n - k, {n, 23}, {k, 0, n}]] // Flatten (* Michael De Vlieger, Apr 10 2018 *)

Prog

(GAP) a:=Filtered(Flat(List([1..10], n->List([1..n], k->k^2+n-k))), IsPrime); # Muniru A Asiru, Apr 09 2018

Crossrefs

Row n: A027753 (n=3), A027755 (n=5), A048059 (n=11), A007635 (n=17), A005846 (n=41).

Cf. A000040, A014556, A302826.

Sequence in context: A117530 A238256 A239277 * A094749 A096539 A338141

Adjacent sequences: A302442 A302443 A302444 * A302446 A302447 A302448

Keyword

nonn,tabf

Author

Seiichi Manyama, Apr 08 2018

Status

approved