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%I #2 Mar 30 2012 17:30:39
%S 4,23,176,1513,14457,166587,2248791,32564154,503597430,8788183110,
%T 170834934690,3490028350200,74757188482200,1750213790778600,
%U 42713495459510400,1084838134027536000,28630810173210336000
%N Determinant of an n X n matrix whose diagonal are the first n composite numbers and all other elements are 1's.
%e The determinant begins:
%e 4 1 1 1 1 1 1 ...
%e 1 6 1 1 1 1 1 ...
%e 1 1 8 1 1 1 1 ...
%e 1 1 1 9 1 1 1 ...
%e 1 1 1 1 10 1 1 ...
%e 1 1 1 1 1 12 1 ...
%t Composite[ n_Integer ] := FixedPoint[ n + PrimePi[ # ] + 1 &, n + PrimePi[ n ] + 1 ]; Table[ Det[ DiagonalMatrix[ Table[ Composite[ i ] - 1, {i, 1, n} ] ] + 1 ], {n, 1, 20} ]
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jan 28 2002