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%I #18 Jun 27 2024 01:34:31
%S 3,5,7,11,13,17,19,23,29,31,37,41,43,53,2539,936599,127852322431,
%T 510819260848900502567,1553192364608434843485965159509450536731,
%U 52119893982548112392303882371161186032080710958633917215400463948724068502699
%N Slowest-growing sequence of odd primes p where 1/(p+1) sums to 1 without actually reaching it.
%C 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.)
%H Amiram Eldar, <a href="/A225670/b225670.txt">Table of n, a(n) for n = 1..23</a>
%t 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]
%Y Similar to A075442, A181503, A225669.
%Y Cf. A000058.
%Y See also A046689.
%K nonn
%O 1,1
%A _Jonathan Sondow_, May 11 2013