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

1,2

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A001223, A064442.

Sequence in context: A010638 A123961 A020763 * A244336 A137323 A021075

Adjacent sequences: A229908 A229909 A229910 * A229912 A229913 A229914

Keyword

nonn,cons,easy

Author

Paolo P. Lava, Oct 03 2013

Status

approved