A302445 -id:A302445 - cp's OEIS frontend

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

Seiichi Manyama, Apr 14 2018

nonn

			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

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

Cf. A014556, A188424, A302445.

A382210 Irregular triangle read by rows: T(n,k) = k^2 - k + (A003173(n) + 1)/4 with 1 <= k < (A003173(n) + 1)/4.

Original entry on oeis.org

2, 3, 5, 5, 7, 11, 17, 11, 13, 17, 23, 31, 41, 53, 67, 83, 101, 17, 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, 1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601

Offset: 4

Stefano Spezia, Mar 18 2025

			The irregular triangle begins as:
   2;
   3,  5;
   5,  7, 11, 17;
  11, 13, 17, 23, 31, 41, 53, 67, 83, 101;
  17, 19, 23, 29, 37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227, 257;
  ...

John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 225.

Cf. A003173, A048058, A302445.

Heegner:={1, 2, 3, 7, 11, 19, 43, 67, 163};A003173[n_]:=Part[Heegner,n]; T[n_,k_]:=k^2-k+(A003173[n]+1)/4;Table[T[n,k],{n,4,9},{k,(A003173[n]+1)/4-1}]//Flatten

cp's OEIS Frontend

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

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A382210 Irregular triangle read by rows: T(n,k) = k^2 - k + (A003173(n) + 1)/4 with 1 <= k < (A003173(n) + 1)/4.

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