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%I #55 Feb 21 2024 11:50:31
%S 1,7,0,9,7,5,5,1,2,4,4,7,5,9,3,1,3,0,1,2,6,8,2,5,9,0,7,0,0,9,0,8,0,9,
%T 4,2,1,8,2,5,9,9,9,6,8,9,0,7,7,1,5,5,8,2,7,6,5,7,3,2,5,1,1,2,8,6,3,2,
%U 1,3,6,4,9,5,6,4,4,3,3,6,7,9,1,3,2,2,7,4,6,6,2,7,5,2,4,5,6,4,0,7,9
%N Decimal expansion of the fixed point c = S(c) of S(x) = Sum_{k>=1} (prime(k) - x) / Product_{i=1..k-1} prime(i).
%C S(x) = (1-x)*(1+A064648) + A249270 is linear so the fixed point is unique.
%C With this constant as h(1) = c, sequence h(n+1) = ceiling(h(n)) * (h(n) - ceiling(h(n)) + c) is real numbers with the property that ceiling(h(n)) = prime(n).
%F Equals (A249270 + A064648 + 1)/(A064648 + 2).
%e 1.709755124475931301268259070090809...
%o (PARI) solve(x=1,2,suminf(k=1,(prime(k)-x)/prod(i=1,k-1,prime(i)))-x) \\ _Michal Paulovic_, Dec 28 2023
%Y Cf. A064648, A249270, A000040.
%Y Cf. A341930 (S(3/2)), A340469 (S(2)).
%K nonn,cons
%O 1,2
%A _Antonio Graciá Llorente_, Dec 27 2023