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Search: id:A101948
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| A101948 |
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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). |
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| 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; listen)
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OFFSET
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0,1
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FORMULA
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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.
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EXAMPLE
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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.
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MATHEMATICA
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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]]
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CROSSREFS
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Sequence in context: A061765 A133940 A030978 this_sequence A087475 A019526 A145488
Adjacent sequences: A101945 A101946 A101947 this_sequence A101949 A101950 A101951
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KEYWORD
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base,nonn,easy
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AUTHOR
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Orges Leka (oleka(AT)students.uni-mainz.de), Dec 22 2004
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EXTENSIONS
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Edited and extended by David Wasserman (dwasserm(AT)earthlink.net), Mar 31 2008
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