A081411 Partial product of prime gaps: a(n) = a(n-1)*(prime(n+1) - prime(n)).

1, 2, 4, 16, 32, 128, 256, 1024, 6144, 12288, 73728, 294912, 589824, 2359296, 14155776, 84934656, 169869312, 1019215872, 4076863488, 8153726976, 48922361856, 195689447424, 1174136684544, 9393093476352, 37572373905408, 75144747810816, 300578991243264, 601157982486528

Offset: 1

Author

Labos Elemer, Apr 01 2003

Keywords

• nonn

Comments

Original name was: Generated by recursion: a(n)=(Mod[Prime[n+1],Prime[n]]*n[n-1]; a[0]=1; Product of the first n consecutive prime-differences.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1244

Crossrefs

Cf. A001223, A080374, A080375, A080376, A099002.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] * (Prime[n + 1] - Prime[n]); Array[a, 30] (* Amiram Eldar, Nov 19 2020 *)

PARI

diff(v)=vector(#v-1,i,v[i+1]-v[i])
pprod(v)=my(t=1); vector(#v,i,t*=v[i])
pprod(diff(primes(50))) \\ Charles R Greathouse IV, Mar 27 2014

Formula

Sum_{n>=1} 1/a(n) = A099002. - Amiram Eldar, Nov 19 2020

Extensions

New name from Charles R Greathouse IV, Mar 27 2014

More terms from Amiram Eldar, Nov 19 2020