|
| |
|
|
A002815
|
|
a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720.
(Formerly M2523 N0996)
|
|
2
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| 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.
|
|
|
REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| 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.
|
|
|
MATHEMATICA
| Table[n + Sum[PrimePi[k], {k, 1, n}], {n, 0, 50}]
|
|
|
CROSSREFS
| Cf. A000720.
Sequence in context: A123753 A124288 A205726 * A109512 A025205 A024190
Adjacent sequences: A002812 A002813 A002814 * A002816 A002817 A002818
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), Mira Bernstein (mira(AT)math.berkeley.edu)
|
| |
|
|
