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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). 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 (list; graph; refs; listen; history; text; internal format)
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: A133940 A174398 A030978 * A087475 A019526 A242014

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

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Last modified February 16 14:47 EST 2019. Contains 320163 sequences. (Running on oeis4.)