A101948 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).

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..97.

Formula

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.

For n >= b^2, f(n, b) = 0.

Example

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.

Mathematica

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]]

Crossrefs

Sequence in context: A174398 A341420 A030978 * A348484 A087475 A019526

Adjacent sequences: A101945 A101946 A101947 * A101949 A101950 A101951

Keyword

base,nonn,easy

Author

Orges Leka (oleka(AT)students.uni-mainz.de), Dec 22 2004

Extensions

Edited and extended by David Wasserman, Mar 31 2008

Status

approved