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A007504
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Sum of first n primes.
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165
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2, 5, 10, 17, 28, 41, 58, 77, 100, 129, 160, 197, 238, 281, 328, 381, 440, 501, 568, 639, 712, 791, 874, 963, 1060, 1161, 1264, 1371, 1480, 1593, 1720, 1851, 1988, 2127, 2276, 2427, 2584, 2747, 2914, 3087, 3266, 3447, 3638, 3831, 4028, 4227, 4438, 4661, 4888
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(A051838(n)) = A002110(A051838(n)) / A116536(n). [Reinhard Zumkeller, Oct 03 2011]
It appears that a(n+1)^2 - a(n)^2 = A034960(n). [From Gary Detlefs, Dec 20 2011]
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REFERENCES
| H. L. Nelson, "Prime Sums", J. Rec. Math., 14 (1981), 205-206.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. J. Mathar, Table of n, a(n) for n = 1..100000
R. J. Mathar, Table of 100000n, a(100000n) for n =1..10000
Nilotpal Kanti Sinha, On the asymptotic expansion of the sum of the first n primes.
Eric Weisstein's World of Mathematics, Prime Sums
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FORMULA
| a(n) has the asymptotic expression a(n) ~ n^2 * log(n) / 2. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 24 2001
a(n) = A014284(n+1) - 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 19 2009]
a(n+1) - a(n) = A000040(n+1). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 19 2009]
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MAPLE
| s1:=[2]; for n from 2 to 1000 do s1:=[op(s1), s1[n-1]+ithprime(n)]; od: s1;
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MATHEMATICA
| Accumulate[Prime[Range[100]]] (* Zak Seidov, Apr 10 2011 *)
a=0; Table[a=a+Prime[k], {k, 100}](* Zak Seidov, Apr 16 2011 *)
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PROG
| (PARI) A007504(n) = sum(k=1, n, prime(k)) [From Michael B. Porter (michael_b_porter(AT)yahoo.com), Feb 26 2010]
(MAGMA) [&+[ NthPrime(k): k in [1..n]]: n in [1..100]]; // Bruno Berselli, Apr 11 2011
(Haskell)
a007504 n = a007504_list !! (n-1)
a007504_list = scanl1 (+) a000040_list -- Reinhard Zumkeller, Oct 03 2011
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CROSSREFS
| Cf. A000041, A034386, A111287. See A122989 for the value of Sum_{ n >= 1} 1/a(n).
Sequence in context: A062493 A056871 A174910 * A172059 A172435 A049688
Adjacent sequences: A007501 A007502 A007503 * A007505 A007506 A007507
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 11 2006
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