A003067 Problimes (second definition). (Formerly M1037)

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

Offset

1,1

Comments

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.

References

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=1..1000

M. D. Hirschhorn, How unexpected is the prime number theorem?, Amer. Math. Monthly, 80 (1973), 675-677.

M. D. Hirschhorn, How unexpected is the prime number theorem?, Amer. Math. Monthly, 80 (1973), 675-677. [Annotated scanned copy]

R. C. Vaughan, The problime number theorem, Bull. London Math. Soc., 6 (1974), 337-340.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Maple

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: # James A. Sellers, Mar 07 2000

Mathematica

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}] (* Jean-François Alcover, Mar 09 2012, after James A. Sellers *)

Crossrefs

Cf. A003066, A003068.

Sequence in context: A127762 A137281 A287420 * A130243 A061465 A368784

Adjacent sequences: A003064 A003065 A003066 * A003068 A003069 A003070

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Mar 07 2000

Status

approved