A225670 - OEIS

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

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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 -- seeA000058.)

LINKS

Amiram Eldar,Table of n, a(n) for n = 1..23

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 toA075442,A181503,A225669.

Cf.A000058.