A121049 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.

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

Offset

1,2

Comments

As n approaches infinity, |a(n)|^(1/n) converges to 2, but a(n+1)/a(n) does not appear to converge.

Links

Table of n, a(n) for n=1..35.

Formula

a(n) = Sum_{j=1..n} (-1)^(j+n)*prime(j)*binomial(n,j-1)/2.

Example

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.

Mathematica

Table[ Sum[(-1)^(j + r)Prime[j] Binomial[r, j - 1]/2, {j, r}], {r, 50}]

Crossrefs

Sequence in context: A327544 A202076 A199825 * A056415 A242993 A366045

Adjacent sequences: A121046 A121047 A121048 * A121050 A121051 A121052

Keyword

easy,sign

Author

Joseph Van Name (prism720(AT)yahoo.com), Aug 08 2006

Extensions

Edited and extended by David Wasserman, Aug 16 2006

Corrected by N. J. A. Sloane, Oct 29 2006

Status

approved