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%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