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%I #2 Mar 31 2012 10:23:54
%S 2,1,3,1,7,5,1,131,23,7,1,165619,1275,59,11,1,1443643414307,8716707,
%T 6843,119,13,1,1930155333520916730618052608,1337002832135523,
%U 153383955,22419,191,17,1
%N Antidiagonally reading the array, formed via: first, writing the primes in the first row (row_1), and forming all successive rows' elements using the previous rows' elements as: row_2(j) = row_1(j)*row_1(j+1) - row_1(j) - row_1(j+1), and so on. The first 'column' of the array, 2 1 -1 -1 -1 -1 -1 -1 ... is converted to its absolute value.
%C The actual array that leads to the list given above is:
%C 2 3 5 7 11 13 17 19 ...
%C 1 7 23 59 119 191 287 395 ...
%C 1 131 1275 6843 22419 54339 112683 241915 ...
%C 1 165619 8716707 ...
%C 1 1443643414307 ...
%C It can be observed that:
%C 1) Obviously, all primes will appear in the list at least once, as the first row of the generating array is composed of all the primes.
%C 2) There exist primes that appear more than once (e.g., 23, 59, 131, 191...).
%C 3) When we have two successive primes in a row, prime(i) & prime(i+1) -as in all of the first row, and occasionally in other rows- the element just below these two is, obviously, Euler_tot( prime(i) * prime (i+1) ) - 1.
%Y Cf. A000040: The list of prime numbers is the first row of the array, that is converted to the list. Cf. A037165: This list, "Prime(n)*prime(n+1)-prime(n)-prime(n+1)" is the second row of the array, that is converted to the list.
%K nonn,tabl
%O 1,1
%A _Umut Uludag_, Sep 17 2009
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