A146985 Triangle T(n,m) = f(n-m)*f(n), where f(n) = A008578(n+1).

1, 2, 2, 3, 4, 3, 5, 6, 6, 5, 7, 10, 9, 10, 7, 11, 14, 15, 15, 14, 11, 13, 22, 21, 25, 21, 22, 13, 17, 26, 33, 35, 35, 33, 26, 17, 19, 34, 39, 55, 49, 55, 39, 34, 19, 23, 38, 51, 65, 77, 77, 65, 51, 38, 23, 29, 46, 57, 85, 91, 121, 91, 85, 57, 46, 29

Offset: 0

Author

Roger L. Bagula, Nov 04 2008

Keywords

• easy
• nonn
• tabl

Comments

I call this sequence "symmetrical spooky primes" as two prime combinations are used in cryptography.

Row sums are:{1, 4, 10, 22, 43, 80, 137, 222, 343, 508, 737}. The sequence to Floor[n/2] is a way to get all the combinations of primes with one less than the other.

Examples

			Triangle T(n,m), n, m >= 0 begins:
   1
   2,  2
   3,  4,  3
   5,  6,  6,  5
   7, 10,  9, 10,  7
  11, 14, 15, 15, 14,  11
  13, 22, 21, 25, 21,  22, 13
  17, 26, 33, 35, 35,  33, 26, 17
  19, 34, 39, 55, 49,  55, 39, 34, 19
  23, 38, 51, 65, 77,  77, 65, 51, 38, 23
  29, 46, 57, 85, 91, 121, 91, 85, 57, 46, 29
		

Programs

Mathematica

Clear[f, t, n, m]; f[n_] := If[n == 0, 1, Prime[n]]; t[n_, m_] = f[n - m]*f[m]; Table[t[n, m], {n, 0, 10}, {m, 0, n}]; Flatten[%]

Extensions

Edited by Peter Munn, Jun 29 2023