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%I #14 Nov 19 2020 04:37:39
%S 1,2,4,16,32,128,256,1024,6144,12288,73728,294912,589824,2359296,
%T 14155776,84934656,169869312,1019215872,4076863488,8153726976,
%U 48922361856,195689447424,1174136684544,9393093476352,37572373905408,75144747810816,300578991243264,601157982486528
%N Partial product of prime gaps: a(n) = a(n-1)*(prime(n+1) - prime(n)).
%C 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.
%H Amiram Eldar, <a href="/A081411/b081411.txt">Table of n, a(n) for n = 1..1244</a>
%F Sum_{n>=1} 1/a(n) = A099002. - _Amiram Eldar_, Nov 19 2020
%t a[1] = 1; a[n_] := a[n] = a[n - 1] * (Prime[n + 1] - Prime[n]); Array[a, 30] (* _Amiram Eldar_, Nov 19 2020 *)
%o (PARI) diff(v)=vector(#v-1,i,v[i+1]-v[i])
%o pprod(v)=my(t=1); vector(#v,i,t*=v[i])
%o pprod(diff(primes(50))) \\ _Charles R Greathouse IV_, Mar 27 2014
%Y Cf. A001223, A080374, A080375, A080376, A099002.
%K nonn
%O 1,2
%A _Labos Elemer_, Apr 01 2003
%E New name from _Charles R Greathouse IV_, Mar 27 2014
%E More terms from _Amiram Eldar_, Nov 19 2020
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