A302826 a(n) is number of primes of form k^2 + n - k for 0 < k < n.

1, 2, 0, 4, 0, 4, 0, 2, 0, 10, 0, 4, 0, 3, 0, 16, 0, 6, 0, 5, 0, 10, 0, 10, 0, 5, 0, 13, 0, 14, 0, 3, 0, 10, 0, 16, 0, 7, 0, 40, 0, 8, 0, 6, 0, 26, 0, 12, 0, 9, 0, 19, 0, 14, 0, 9, 0, 34, 0, 21, 0, 5, 0, 19, 0, 36, 0, 13, 0, 28, 0, 18, 0, 7, 0, 31, 0, 18, 0, 19, 0, 34, 0, 15

Offset

2,2

Links

Seiichi Manyama, Table of n, a(n) for n = 2..10000

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

Wikipedia, Lucky numbers of Euler

Example

Primes of form k^2 + n - k for 0 < k < n:
  n\k|  1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16  |a(n)
  ---+------------------------------------------------------------------------+----
    2|  2;                                                                    |  1
    3|  3,  5;                                                                |  2
    4|                                                                        |  0
    5|  5,  7, 11, 17;                                                        |  4
    6|                                                                        |  0
    7|  7,   , 13, 19,   , 37;                                                |  4
    8|                                                                        |  0
    9|   , 11,   ,   , 29,   ,   ,   ;                                        |  2
   10|                                                                        |  0
   11| 11, 13, 17, 23, 31, 41, 53, 67, 83, 101;                               | 10
   12|                                                                        |  0
   13| 13,   , 19,   ,   , 43,   ,   ,   , 103,    ,    ;                     |  4
   14|                                                                        |  0
   15|   , 17,   ,   ,   ,   ,   , 71,   ,    ,    ,    ,    , 197;           |  3
   16|                                                                        |  0
   17| 17, 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257; | 16

Crossrefs

Cf. A014556, A188424, A302445.

Sequence in context: A349240 A366879 A109578 * A332903 A082519 A035688

Adjacent sequences: A302823 A302824 A302825 * A302827 A302828 A302829

Keyword

nonn

Author

Seiichi Manyama, Apr 14 2018

Status

approved