A003067 Problimes (second definition).

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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

Crossrefs

Cf. A003066, A003068.

Programs

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 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 Sellers *)

Extensions

More terms from James Sellers, Mar 07 2000