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%I #5 Mar 30 2012 17:38:04
%S 4,5,8,13,20,4,1,16,49,100,16,1,4,25,64,36,9,0,9,36,64,25,4,1,16,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N For any n >= 0 and b >= 2, let k be the length of the base-b expansion of n and let M(n, b) be the 2 X k matrix whose first row contains the first k primes in descending order and whose second row contains the base-b expansion of n. Let f(n, b) = determinant[transpose(M(n, b))*M(n, b)]. Sequence gives f(n, 5).
%F For 0 <= x < b, 1 <= y < b, f(x, b) = x^2+4 and f(yb+x, b) = 4*x^2+9*y^2-12*x*y.
%F For n >= b^2, f(n, b) = 0.
%e M(21, 5) = [3,2; 4,1], so a(21) = det([3,4; 2,1]*[3,2; 4,1]) = det([25,10; 10,5]) = 25.
%t Generating A(n, b): A[n_Integer, base_Integer]/;base>=2:= {Prime[Range[Length[IntegerDigits[n, base]]1, -1]], IntegerDigits[n, base]} computing the determinant: Det[Transpose[A[n, b]].A[n, b]] then b = 5 and a(n) = Det[Transpose[A[n, 5]].A[n, 5]]
%K base,nonn,easy
%O 0,1
%A Orges Leka (oleka(AT)students.uni-mainz.de), Dec 22 2004
%E Edited and extended by _David Wasserman_, Mar 31 2008
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