

A101948


For any n >= 0 and b >= 2, let k be the length of the baseb 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 baseb expansion of n. Let f(n, b) = determinant[transpose(M(n, b))*M(n, b)]. Sequence gives f(n, 5).


0



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
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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^212*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: A133940 A174398 A030978 * A087475 A019526 A242014
Adjacent sequences: A101945 A101946 A101947 * A101949 A101950 A101951


KEYWORD

base,nonn,easy


AUTHOR

Orges Leka (oleka(AT)students.unimainz.de), Dec 22 2004


EXTENSIONS

Edited and extended by David Wasserman, Mar 31 2008


STATUS

approved



