A058077 Binomial coefficients formed from consecutive primes: a(n) = binomial( prime(n+1), prime(n) ).

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

Offset: 1

Author

Labos Elemer, Nov 13 2000

Keywords

• nonn

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

Examples

			n=6: a(6) = C(p(7),p(6)) = C(17,13) = 57120/24 = 2380.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms (where the color is function of A001223(n))

Crossrefs

Cf. A000040, A001223.

Cf. A037293, A066526, A080911, A277341.

Programs

Mathematica

Table[Binomial[Prime[n+1],Prime[n]],{n,1,20}] (* Vaclav Kotesovec, Nov 13 2014 *)

Formula

a(n) = binomial(A000040(n+1), A001223(n)).

Extensions

Offset corrected by Vaclav Kotesovec, Nov 13 2014