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Search: id:A007504
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| A007504 |
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Sum of first n primes.
(Formerly M1370)
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+0
142
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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; listen)
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OFFSET
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1,1
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REFERENCES
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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
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R. J. Mathar, Table of n, a(n) for n = 1..100000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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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) = (n+1)-th primes. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 19 2009]
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MAPLE
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s1:=[2]; for n from 2 to 1000 do s1:=[op(s1), s1[n-1]+ithprime(n)]; od: s1;
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MATHEMATICA
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Table[Sum[Prime[i], {i, 1, n}], {n, 1, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 11 2006
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CROSSREFS
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Cf. A000041, A034386, A111287. See A122989 for the value of Sum_{ n >= 1} 1/a(n).
Sequence in context: A119114 A062493 A056871 this_sequence A049688 A011894 A071602
Adjacent sequences: A007501 A007502 A007503 this_sequence A007505 A007506 A007507
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 11 2006
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