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Search: id:A002815
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| A002815 |
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a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720.
(Formerly M2523 N0996)
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+0
1
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| 0, 1, 3, 6, 9, 13, 17, 22, 27, 32, 37, 43, 49, 56, 63, 70, 77, 85, 93, 102, 111, 120, 129, 139, 149, 159, 169, 179, 189, 200, 211, 223, 235, 247, 259, 271, 283, 296, 309, 322, 335, 349, 363, 378, 393, 408, 423, 439, 455, 471
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The g.f. (-1+z**7+z**8-z**4-z**2-z)/(z+1)/(z**2-z+1)/(z**2+z+1)/(z-1)**3 conjectured by S. Plouffe in his 1992 dissertation is wrong.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
H. Brocard, Reply to Query 1421, Nombres premiers dans une suite de differences, L'Interm\'{e}diaire des Math\'{e}maticiens, 7 (1900), 135-137.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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MATHEMATICA
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Table[n + Sum[PrimePi[k], {k, 1, n}], {n, 0, 50}]
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CROSSREFS
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Cf. A000720.
Sequence in context: A061781 A123753 A124288 this_sequence A109512 A025205 A024190
Adjacent sequences: A002812 A002813 A002814 this_sequence A002816 A002817 A002818
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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), Mira Bernstein (mira(AT)math.berkeley.edu)
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