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A141042
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Product of n and the n-th gap between primes: a(n) = n*A001223(n).
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13
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1, 4, 6, 16, 10, 24, 14, 32, 54, 20, 66, 48, 26, 56, 90, 96, 34, 108, 76, 40, 126, 88, 138, 192, 100, 52, 108, 56, 116, 420, 124, 192, 66, 340, 70, 216, 222, 152, 234, 240, 82, 420, 86, 176, 90, 552, 564, 192, 98, 200, 306, 104
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OFFSET
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1,2
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COMMENTS
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a(n) is also the area under the curve of the function pi(x) from prime(n) to prime(n+1), see the illustration of initial terms. This sequence is also the first differences of A152535. - Omar E. Pol, Nov 13 2013
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LINKS
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FORMULA
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EXAMPLE
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a(5)=10 because the 5th prime is 11 and the 6th prime is 13. The 5th gap between primes is 2, then a(5)=5*2=10.
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MAPLE
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P:= [seq(ithprime(i), i=1..1001)]:
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MATHEMATICA
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Table[n*(Prime[n+1] - Prime[n]), {n, 100}] (* T. D. Noe, Nov 14 2013 *)
With[{nn=60}, Times@@@Thread[{Range[nn], Differences[Prime[Range[nn+1]]]}]] (* Harvey P. Dale, Dec 18 2018 *)
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PROG
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(PARI) diff(v)=vector(#v-1, i, (v[i+1]-v[i])*i);
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Corrected definition and example. - Omar E. Pol, Nov 16 2008
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STATUS
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approved
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