A181503 Slowest-growing sequence of primes p where 1/(p+1) sums to 1 without actually reaching it.

2, 3, 5, 7, 11, 29, 127, 1931, 309121, 47777896349, 76090912606600214447, 120621395443859821620817698234224534627, 63813688766771960235613705494151343867425896610637722399417500492543759703

Offset: 1

Author

Aaron Meyerowitz, Oct 24 2010

Keywords

• nice
• nonn

Comments

The sum of 1/(p+1) over p = 2, 3, 5, 7, 11, 23 = A046689 is exactly 1.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..17 . [From _Robert G. Wilson v_, Oct 27 2010]

Crossrefs

Similar to A075442. See also A046689.

Programs

Mathematica

a[n_] := a[n] = Block[{sm = Sum[1/(a[i] + 1), {i, n - 1}]}, NextPrime[ Max[ a[n - 1], 1/(1 - sm)]]]; a[0] = 1; Array[a, 15] (* Robert G. Wilson v, Oct 27 2010 *)

Extensions

a(12) onwards from Robert G. Wilson v, Oct 27 2010