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Search: id:A121049
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| A121049 |
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Let p_n be the polynomial of degree n-1 that interpolates the first n primes (i.e. p_n(i) = prime(i) for 1 <= i <= n.) Then a(n) = p_n(n+1)/2. |
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+0
1
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| 1, 2, 4, 4, 11, -3, 36, -46, 133, -213, 419, -586, 716, -199, -1807, 7570, -20637, 47563, -97849, 185438, -326192, 531721, -785058, 980926, -780084, -700944, 5511613, -18000159, 46704269, -107137804, 225187101, -439627178, 799622938, -1347732434, 2069035230
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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As n approaches infinity |a(n)|^(1/n) converges to 2, but a(n+1)/a(n) does not appear to converge.
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FORMULA
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a(n) = Sum_{j=1..n} (-1)^(j+n)*prime(j)*binomial(n,j-1)/2.
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EXAMPLE
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p_3(x) = (x^2-x+4)/2. p_3(1) = 2, p_3(2) = 3, p_3(3) = 5, so
a(3) = p_3(4)/2 = 4.
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MATHEMATICA
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Table[ Sum[(-1)^(j + r)Prime[j] Binomial[r, j - 1]/2, {j, r}], {r, 50}]
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CROSSREFS
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Sequence in context: A126138 A054764 A118336 this_sequence A056415 A000936 A065449
Adjacent sequences: A121046 A121047 A121048 this_sequence A121050 A121051 A121052
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KEYWORD
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easy,sign
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AUTHOR
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Joseph Van Name (prism720(AT)yahoo.com), Aug 08 2006
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EXTENSIONS
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Edited and extended by David Wasserman (dwasserm(AT)earthlink.net), Aug 16 2006
Corrected by N. J. A. Sloane (njas(AT)research.att.com), Oct 29 2006
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