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A058077 Binomial coefficients formed from consecutive primes: a(n) = binomial( prime(n+1), prime(n) ). 15
3, 10, 21, 330, 78, 2380, 171, 8855, 475020, 465, 2324784, 101270, 903, 178365, 22957480, 45057474, 1830, 99795696, 971635, 2628, 277962685, 1837620, 581106988, 144520208820, 4082925, 5253, 5160610, 5886, 6438740 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Conjecture: for each value of n > 1, if a(n+1) has the same number of digits as a(n) and a(n+1) > a(n), then prime(n+2) - prime(n+1) = prime(n+1) - prime(n). This conjecture has been verified for all n < 3*10^7. - Ahmad J. Masad, Oct 08 2019
LINKS
Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms (where the color is function of A001223(n))
FORMULA
a(n) = binomial(A000040(n+1), A001223(n)).
EXAMPLE
n=6: a(6) = C(p(7),p(6)) = C(17,13) = 57120/24 = 2380.
MATHEMATICA
Table[Binomial[Prime[n+1], Prime[n]], {n, 1, 20}] (* Vaclav Kotesovec, Nov 13 2014 *)
CROSSREFS
Sequence in context: A337623 A158030 A068082 * A161672 A190092 A174459
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 13 2000
EXTENSIONS
Offset corrected by Vaclav Kotesovec, Nov 13 2014
STATUS
approved

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Last modified March 1 20:05 EST 2024. Contains 370443 sequences. (Running on oeis4.)