A229911 Decimal expansion of number whose continued fraction expansion is formed by the difference of consecutive primes (A001223).

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, 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, 6, 6, 5, 3, 3, 6, 6, 1, 1, 5, 3, 8, 1, 6, 2, 8, 4, 7, 7

Offset: 1

Author

Paolo P. Lava, Oct 03 2013

Keywords

• nonn
• cons
• easy

Examples

			1.408248346018747844183196249564... = [1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, ...]
		

References

• G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 157.

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001223, A064442.

Programs

Maple

P:=proc(q) local a,n,v; v:=array(1..q); a:=1;
for n from 1 to q do v[n]:=(ithprime(n+1)-ithprime(n)); od;
for n from q by -1 to 1 do a:=v[n]+1/a; od; print(evalf(a,200));
end: P(10^4);

Mathematica

m=200;RealDigits[FromContinuedFraction[Differences[Prime[Range[1001]]]],10,m][[1]] (* Zak Seidov, Oct 04 2013 *)

PARI

diff(v)=vector(#v-1,i,v[i+1]-v[i])
(M->M[1,1]/M[2,1]*1.)(contfracpnqn(diff(primes(100)))) \\ Charles R Greathouse IV, Oct 04 2013