A003068 Problimes (third definition). (Formerly M1038)

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

1,1

Comments

This sequence is like A003066 except the result is rounded up. - Michael B. Porter, Oct 27 2025

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.

Example

For n=4, the approximation is 7 + 1 / ((1-1/2) * (1-1/4) * (1-1/7)) = 10.1111..., which is rounded up to 11, so a(4)=11. - Michael B. Porter, Oct 27 2025

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 *)

Crossrefs

Cf. A003066, A003067.

Sequence in context: A087163 A062467 A250621 * A194168 A347763 A198759

Adjacent sequences: A003065 A003066 A003067 * A003069 A003070 A003071

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from James Sellers, Mar 07 2000

Status

approved