A225670 Slowest-growing sequence of odd primes p where 1/(p+1) sums to 1 without actually reaching it.

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, 2539, 936599, 127852322431, 510819260848900502567, 1553192364608434843485965159509450536731, 52119893982548112392303882371161186032080710958633917215400463948724068502699

Offset

1,1

Comments

Is there a finite set of odd primes p where 1/(p+1) sums exactly to 1? (This would be an analog of 1/(2+1) + 1/(3+1) + 1/(5+1) + 1/(7+1) + 1/(11+1) + 1/(23+1) = 1 -- see A000058.)

Links

Table of n, a(n) for n=1..20.

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] = 2; Array[ a, 20]

Crossrefs

Similar to A075442, A181503, A225669. See also A046689.

Sequence in context: A179429 A020615 A172146 * A165255 A223036 A155058

Adjacent sequences: A225667 A225668 A225669 * A225671 A225672 A225673

Keyword

nonn

Author

Jonathan Sondow, May 11 2013

Status

approved