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A081411
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Partial product of prime gaps: a(n) = a(n-1)*(prime(n+1) - prime(n)).
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3
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..1244
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FORMULA
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Sum_{n>=1} 1/a(n) = A099002. - Amiram Eldar, Nov 19 2020
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = a[n - 1] * (Prime[n + 1] - Prime[n]); Array[a, 30] (* Amiram Eldar, Nov 19 2020 *)
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PROG
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(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
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CROSSREFS
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Cf. A001223, A080374, A080375, A080376, A099002.
Sequence in context: A334083 A274497 A145119 * A269758 A094384 A053038
Adjacent sequences: A081408 A081409 A081410 * A081412 A081413 A081414
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Apr 01 2003
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EXTENSIONS
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New name from Charles R Greathouse IV, Mar 27 2014
More terms from Amiram Eldar, Nov 19 2020
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STATUS
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approved
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