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%I #17 Oct 04 2013 10:46:55
%S 1,4,0,8,2,4,8,3,4,6,0,1,8,7,4,7,8,4,4,1,8,3,1,9,6,2,4,9,5,6,4,8,5,9,
%T 4,4,8,0,2,8,7,8,9,1,3,6,4,1,7,0,9,5,3,4,6,0,5,2,8,6,2,6,5,3,9,1,0,5,
%U 6,6,5,3,3,6,6,1,1,5,3,8,1,6,2,8,4,7,7
%N Decimal expansion of number whose continued fraction expansion is formed by the difference of consecutive primes (A001223).
%D G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 157.
%H Paolo P. Lava, <a href="/A229911/b229911.txt">Table of n, a(n) for n = 1..10000</a>
%e 1.408248346018747844183196249564... = [1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, ...]
%p P:=proc(q) local a,n,v; v:=array(1..q); a:=1;
%p for n from 1 to q do v[n]:=(ithprime(n+1)-ithprime(n)); od;
%p for n from q by -1 to 1 do a:=v[n]+1/a; od; print(evalf(a,200));
%p end: P(10^4);
%t m=200;RealDigits[FromContinuedFraction[Differences[Prime[Range[1001]]]],10,m][[1]] (* _Zak Seidov_, Oct 04 2013 *)
%o (PARI) diff(v)=vector(#v-1,i,v[i+1]-v[i])
%o (M->M[1,1]/M[2,1]*1.)(contfracpnqn(diff(primes(100)))) \\ _Charles R Greathouse IV_, Oct 04 2013
%Y Cf. A001223, A064442.
%K nonn,cons,easy
%O 1,2
%A _Paolo P. Lava_, Oct 03 2013
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