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A099724
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Decimal expansion of the sum_{n>0} of (A000040(n+1)-A000040(n))/exp(n), where A000040(k) gives the k-th prime number and exp(k) is the natural exponential of k.
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0
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8, 3, 8, 9, 0, 9, 8, 2, 7, 5, 9, 2, 1, 6, 4, 1, 8, 9, 3, 2, 7, 6, 7, 7, 5, 9, 3, 3, 0, 5, 4, 2, 8, 2, 3, 8, 5, 5, 1, 1, 9, 4, 0, 3, 5, 9, 7, 4, 1, 8, 4, 8, 5, 0, 9, 2, 2, 2, 5, 0, 2, 9, 3, 7, 4, 3, 3, 3, 5, 3, 7, 4, 9, 9, 4, 7, 8, 0, 3, 7, 6, 5, 1, 2, 7, 8, 7, 5, 9, 6, 8, 3, 4, 4, 9, 7, 2, 8, 8, 0, 2, 5, 3, 8, 7
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Relates the growth of a function giving the difference between successive prime numbers (A000040(n+1)-A000040(n) or A001223(n)) to the growth of the natural exponential exp(n)=e^n where e is Euler's number (A001113).
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FORMULA
| sum((ithprime(i+1)-ithprime(i))/exp(i), i=1..infinity);
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EXAMPLE
| 0.838909827592164189327677593305428238551194035974184850922250293743335374994780376512787596834497288025387...
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MAPLE
| f:=N->sum((ithprime(n+1)-ithprime(n))/exp(n), n=1..N); evalf[106](f(1000)); evalf[106](f(2000));
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CROSSREFS
| Cf. A000040, A001223, A001113.
Sequence in context: A019866 A006833 A085011 * A024568 A166202 A146482
Adjacent sequences: A099721 A099722 A099723 * A099725 A099726 A099727
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KEYWORD
| cons,nonn
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AUTHOR
| Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 07 2004
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