login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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

%I #8 Jun 29 2023 22:11:28

%S 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,

%T 13,17,26,33,35,35,33,26,17,19,34,39,55,49,55,39,34,19,23,38,51,65,77,

%U 77,65,51,38,23,29,46,57,85,91,121,91,85,57,46,29

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

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

%C 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.

%e Triangle T(n,m), n, m >= 0 begins:

%e 1

%e 2, 2

%e 3, 4, 3

%e 5, 6, 6, 5

%e 7, 10, 9, 10, 7

%e 11, 14, 15, 15, 14, 11

%e 13, 22, 21, 25, 21, 22, 13

%e 17, 26, 33, 35, 35, 33, 26, 17

%e 19, 34, 39, 55, 49, 55, 39, 34, 19

%e 23, 38, 51, 65, 77, 77, 65, 51, 38, 23

%e 29, 46, 57, 85, 91, 121, 91, 85, 57, 46, 29

%t 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[%]

%K easy,nonn,tabl

%O 0,2

%A _Roger L. Bagula_, Nov 04 2008

%E Edited by _Peter Munn_, Jun 29 2023