A003068 Problimes (third definition).

2, 4, 7, 11, 15, 19, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 187, 193, 199, 205, 211, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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.

Crossrefs

Cf. A003066, A003067.

Programs

Maple

a[1] := 2: for i from 1 to 150 do a[i+1] := ceil(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] = Ceiling[a[n-1] + 1/Product[1 - 1/a[j], {j, 1, n-1}]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Nov 18 2013 *)

Extensions

More terms from James Sellers, Mar 07 2000