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A003067
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Problimes (second definition).
(Formerly M1037)
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3
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2, 4, 7, 10, 13, 17, 21, 25, 29, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 235, 242, 249, 256, 263, 270, 277, 284, 291, 298, 305, 312, 319
(list;
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refs;
listen;
history;
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OFFSET
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1,1
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COMMENTS
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It would be nice to have a clearer definition. - N. J. A. Sloane, Jul 21 2008
The g.f. (z**2+2+z**9+z**5)/(z-1)**2 conjectured by Simon Plouffe in his 1992 dissertation is wrong.
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REFERENCES
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M. D. Hirschhorn, How unexpected is the prime number theorem?, Amer. Math. Monthly, 80 (1973), 675-677.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. C. Vaughan, The problime number theorem, Bull. London Math. Soc., 6 (1974), 337-340.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
_Simon 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.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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MAPLE
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a[1] := 2: for i from 1 to 150 do a[i+1] := round(a[i]+1/product((1-1/a[j]), j=1..i)): od:
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MATHEMATICA
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a[1] = 2; a[n_] := a[n] = Round[a[n-1] + 1/Product[1-1/a[j], {j, 1, n-1}]]; Table[a[n], {n, 1, 60}] (* From Jean-François Alcover, Mar 09 2012, after James A. Sellers *)
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CROSSREFS
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Cf. A003066, A003068.
Sequence in context: A194236 A127762 A137281 * A130243 A061465 A126022
Adjacent sequences: A003064 A003065 A003066 * A003068 A003069 A003070
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms and Maple code from James A. Sellers, Mar 07 2000
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STATUS
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approved
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